Combinatorial Optimization in Telecommunicationco-at-work.zib.de/berlin2009/downloads/2009-10-05/2009... · 2009-10-05 · Martin Grötschel Institut für Mathematik, Technische Universität
124
Martin Grötschel Institut für Mathematik, Technische Universität Berlin (TUB) DFG-Forschungszentrum „Mathematik für Schlüsseltechnologien“ (MATHEON) Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) [email protected]http://www.zib.de/groetschel Combinatorial Optimization in Telecommunication CO@W Berlin Martin Grötschel 5. 10. 2009 9:00 – 10:30
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
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Todayrsquos program
MartinGroumltschel
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
4
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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5
The beginning Clyde Monma (Bell LabsBell Communications Research) Cornell University 1987
Survivable telecommunications networks
What was the problem
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6 TheBellCorestudy
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The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
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Facets one example
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Facets anotherexample
ge
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Recall The Importance of Facets
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Recall The Importance of Facets
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Real data
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Problem reductions
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Computational results with real data
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LATA DL optimal solutions
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Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
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But then USA 1987-1988(collected by Clyde Monma)
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USA 1987-1988
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Special Report by IEEE Spectrum
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Special Report
IEEE Spectrum
June1988
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Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
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Berlin 1994 amp Koumlln 1994
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High-TechTerrorism 1995
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Berlin 1997 amp Wien
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OumlsterreichAustria
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MediterraneanIceland
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Most recent event in Germany (I know of)
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Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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Mobile Phone Production Line
Fujitsu Nasu plant
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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Component bdquoCablesldquo
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Component bdquoAntennasldquo
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Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
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min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
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53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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Solution Hierarchy amp Backbone
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G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
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Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
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Network Planningdetails later today
MartinGroumltschel
84
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85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
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Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
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100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
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COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
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111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
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113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
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Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Todayrsquos program
MartinGroumltschel
2
COW
MartinGroumltschel
3
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
4
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
5
The beginning Clyde Monma (Bell LabsBell Communications Research) Cornell University 1987
Survivable telecommunications networks
What was the problem
COW
MartinGroumltschel
6 TheBellCorestudy
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
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8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
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43
Component bdquoAntennasldquo
COW
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
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Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
3
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
4
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
5
The beginning Clyde Monma (Bell LabsBell Communications Research) Cornell University 1987
Survivable telecommunications networks
What was the problem
COW
MartinGroumltschel
6 TheBellCorestudy
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
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43
Component bdquoAntennasldquo
COW
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
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59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
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63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
4
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
5
The beginning Clyde Monma (Bell LabsBell Communications Research) Cornell University 1987
Survivable telecommunications networks
What was the problem
COW
MartinGroumltschel
6 TheBellCorestudy
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
5
The beginning Clyde Monma (Bell LabsBell Communications Research) Cornell University 1987
Survivable telecommunications networks
What was the problem
COW
MartinGroumltschel
6 TheBellCorestudy
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
COW
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43
Component bdquoAntennasldquo
COW
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
6 TheBellCorestudy
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
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MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
7
The IP Model minimum cost spanning tree minimum cost Steiner tree min-cost k-edge or k-node-connected subgraph
Special cases
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
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MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
8
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
9
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
COW
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
10
Facets one example
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
11
Facets anotherexample
ge
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Recall The Importance of Facets
MartinGroumltschel
12
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
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MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
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MartinGroumltschel
20
USA 1987-1988
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MartinGroumltschel
21
Special Report by IEEE Spectrum
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MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
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MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
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MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
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MartinGroumltschel
25
High-TechTerrorism 1995
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MartinGroumltschel
26
Berlin 1997 amp Wien
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MartinGroumltschel
27
OumlsterreichAustria
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MediterraneanIceland
MartinGroumltschel
28
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Most recent event in Germany (I know of)
MartinGroumltschel
29
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MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Recall The Importance of Facets
MartinGroumltschel
13
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
14
Real data
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
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MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
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MartinGroumltschel
20
USA 1987-1988
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MartinGroumltschel
21
Special Report by IEEE Spectrum
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MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
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MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
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MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
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MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
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COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
15
Problem reductions
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
16
Computational results with real data
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
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MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
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MartinGroumltschel
20
USA 1987-1988
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MartinGroumltschel
21
Special Report by IEEE Spectrum
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MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
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MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
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MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
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MartinGroumltschel
25
High-TechTerrorism 1995
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MartinGroumltschel
26
Berlin 1997 amp Wien
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MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
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MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
17
LATA DL optimal solutions
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
18
Problem Nobody at Bell was interested (except for the scientists)
We were too much ahead of time
But then
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
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22
Special Report
IEEE Spectrum
June1988
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MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
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MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
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MartinGroumltschel
25
High-TechTerrorism 1995
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26
Berlin 1997 amp Wien
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MartinGroumltschel
27
OumlsterreichAustria
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MediterraneanIceland
MartinGroumltschel
28
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Most recent event in Germany (I know of)
MartinGroumltschel
29
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30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
19
But then USA 1987-1988(collected by Clyde Monma)
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
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MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
20
USA 1987-1988
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
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Most recent event in Germany (I know of)
MartinGroumltschel
29
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MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
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MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
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MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
21
Special Report by IEEE Spectrum
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
22
Special Report
IEEE Spectrum
June1988
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
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MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
23
Not unfrequent in industry
Dont bother me with new ideas I have a battle to fight
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
24
Berlin 1994 amp Koumlln 1994
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
25
High-TechTerrorism 1995
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
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56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
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57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
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71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
26
Berlin 1997 amp Wien
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
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GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
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Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
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MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
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MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
27
OumlsterreichAustria
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MediterraneanIceland
MartinGroumltschel
28
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Most recent event in Germany (I know of)
MartinGroumltschel
29
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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COW
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
30
Industry PartnersBell Communications Research (now Telcordia) amp ATampT
Telenor (Norwegian Telecom)
E-Plus
DFN-Verein
Detecon International GmbH
Bosch Telekom
Siemens
Austria Telekom
T-Systems Nova (T-Systems Deutsche Telekom)
KPN
Telecel-Vodafone
atesio (ZIB spin-off company)
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
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COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
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Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
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Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
31
The Telecom-GroupManfred BrandtAndreas EisenblaumltterMartin GroumltschelThorsten KochMaren MartensChristian RaackAxel WernerRoland Wessaumlly
Former Team MembersDimitris Alevras (ZIB IBM)Norbert Ascheuer (ZIB atesio)Andreas Bley (ZIB TU Berlin)Hans Florian Geerdes (ZIB Booz Allen)Tobias Harks (ZIB TU Berlin)Christoph Helmberg (ZIB U Chemnitz)Arie Koster (ZIB RWTH Aachen) Sven Krumke (ZIB TU Kaiserslautern)Alexander Martin (ZIB TU Darmstadt)Mechthild Opperud (ZIB Telenor)Sebastian Orlowski (ZIB atesio)Diana Poensgen (ZIB McKinsey)Joumlrg Rambau (ZIB U Bayreuth)Adrian Zymolka (ZIB Axioma)
The ZIBMATHEON Telecom-Team
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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42
Component bdquoCablesldquo
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43
Component bdquoAntennasldquo
COW
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44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
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61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
32
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
33
Advertisement Modern telecommunication is impossible without mathematics
Cryptography digital signal encoding queue management come to your mind immediately
But modern mathematics also supports the innovative design and the cost-efficient production of devices and equipment Mathematics plans low-cost high-capacity survivable networks and optimizes their operation
Briefly no efficient use of scarce resources without mathematics ndashnot only in telecommunication
Many of these achievements are results of newest research Their employment in practice is fostered by significant improvements in computing technology
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
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MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
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MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
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MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
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MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
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MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
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MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
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MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
34
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
SpeechData
VideoEtc
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
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MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
35
What is the Telecom Problem
Design excellent technical devicesand a robust network that survivesall kinds of failures and organize the traffic such that high quality telecommunication betweenvery many individual units at many locations is feasibleat low cost
This problem is too general
to be solved in one step
Approach in Practice Decompose whenever possible Look at a hierarchy of problems Address the individual problems one by one Recompose to find a good global solution
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
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COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
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Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
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Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
36
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
37
Cell Phones and Mathematics
Designing mobile phonesTask partitioningChip design (VLSI)Component design
Computational logicCombinatorial
optimizationDifferential algebraic
equations
Producing Mobile PhonesProduction facility layoutControl of CNC machinesControl of robots Lot sizingSchedulingLogistics
Operations researchLinear and integer programmingCombinatorial optimizationOrdinary differential equations
Marketing and Distributing MobilesFinancial mathematics Transportation optimization
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
38
Production and Mathematics ExamplesCNC Machine for 2D and 3D
cutting and welding(IXION ULM 804)
Sequencing of Tasksand Optimization of Moves
Mounting DevicesMinimizing Production Time
via TSP or IP
Printed Circuit Boards
Optimization of Manufacturing
SMD
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
39
Mobile Phone Production Line
Fujitsu Nasu plant
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
40
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
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MartinGroumltschel
43
Component bdquoAntennasldquo
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MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
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MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
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65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
41
Network Components
Design Production Marketing DistributionSimilar math problems as for mobile phones
Fiber (and other) cablesAntennas and Transceivers Base stations (BTSs)Base Station Controllers (BSCs)Mobile Switching Centers (MSCs)and more
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
42
Component bdquoCablesldquo
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
43
Component bdquoAntennasldquo
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
44
Component bdquoBase Stationldquo
Nokia MetroSite
Nokia UltraSite
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
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MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
45
ComponentbdquoMobile Switching Centerldquo
Example of an MSC Plan
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
46
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
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MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
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MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
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93
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94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
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COW
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
47
Network Design Tasks to be solvedSome Examples
Locating the sites for antennas (TRXs) and base transceiver stations (BTSs)
Assignment of frequencieschannels to antennas
Cryptography and error correcting encoding for wireless communication
Clustering BTSs
Locating base station controllers (BSCs)
Connecting BTSs to BSCs
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
48
Network Design Tasks to be solved Some Examples (continued) Locating Mobile Switching Centers (MSCs)
Clustering BSCs and Connecting BSCs to MSCs
Designing the BSC network (BSS) and the MSC network (NSS or core network) Topology of the network
Capacity of the links and components
Routing of the demand
Survivability in failure situations
Most of these problems turn out to be Combinatorial Optimization or
Mixed Integer Programming Problems
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
49
Connecting Mobiles Whatacutes up
BSC
MSC
BSC
BSC
BSC
BSC
BSC
BSC
MSC
MSCMSC
MSC
BTS
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
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MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
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COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
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Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
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Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
50
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
51
Frequency or Channel AssignmentRadio InterfaceAndreas Eisenblaumltter will lecture on this aspect in detail eg about
GSM technology(GSM = Global System for Mobile Communications)
UMTS (UMTS = Universal Mobile Telecommunications System)a system that is based on CDMA technology(CDMA = Code Division Multiple Access)which is currently being deployed
and more
Eisenblaumltter Andreas Frequency Assignment in GSM Networks Models Heuristics and Lower Bounds 2001 (awarded with the INFORMS Telecommunications Dissertation Award and the Dissertation Prize of the Gesellschaft fuumlr Operations Research 2002)
Geerdes Hans-Florian UMTS Radio Network Planning Mastering Cell Coupling for Capacity Optimization PhD Thesis TU Berlin 2008(Dissertationspreis 2008 der von der Gesellschaft fuumlr Informatik (GI) und der Informationstechnischen Gesellschaft (ITG) gemeinsam getragenen Fachgruppe Kommunikation und Verteilte Systeme)
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
GSM Minimum InterferenceFrequency Assignment Problem (FAP)FAP is an Integer Linear Program
MartinGroumltschel
52
min
1
1 ( )1 1 1
01
isin isin
isin
+
= forall isin
+ le forall isin minus lt
+ le + forall isin isin cap
+ le + forall isin minus =
isin
sum sumsum
co ad
v
co co ad advw vw vw vw
vw E vw E
vff F
dwgvf
co covw v wvf wfad ad
wg vwvfco advw vwvf
c z c z
s t x v V
x x vw E f g d vwx x z vw E f F Fx x z vw E f gx z z
that is very difficult to solve
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
MartinGroumltschel
53
GSM Region Berlin - Dresden
2877 antennas
50 channels
interference reduction
836
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
54
UMTS Configuration of Antennas
path loss
IsotropicPrediction
Antenna Prediction Available for each potential antenna location
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG
copy Digital Building Model Berlin (2002) E-Plus Mobilfunk GmbH amp Co KG Germany
AntennaDiagram Signal propagation
in different directions
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
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MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
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MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Optimization Reduction of UMTS Network Load
Start-Configuration
Adjustment
Azimuth
Direction
Optimized Configuration
0
20
TXpower[W]
Reduction
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
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MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
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MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
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MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
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MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
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MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
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X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
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Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
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Number of Nodes in the Core Network
MartinGroumltschel
91
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Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
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MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
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MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
56
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
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MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
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MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
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MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
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MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
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82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
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Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
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Number of Nodes in the Core Network
MartinGroumltschel
91
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Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
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X-Win Backbone January 2009
MartinGroumltschel
93
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94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
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MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
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MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
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MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
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111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
57
G-WiN DataG-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein
Internet access of all German universities and research institutions
Locations to be connected 750 Data volume in summer 2000 220 Terabytesmonth Expected data volume in 2004 10000 Terabytesmonth
Clustering (to design a hierarchical network) 10 nodes in Level 1a 261 nodes eligible for 20 nodes in Level 1b Level 1 All other nodes in Level 2
Bley Andreas Koch Thorsten Optimierung in der Planung und beim Aufbau des G-WiN DFN-Mitteilungen H 54 2000 13-15
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
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MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
58
G-WiN Problem
Select the 10 nodes of Level 1a Select the 20 nodes of Level 1b
Each Level 1a node has to be linked to two Level 1b nodes Link every Level 2 node to one Level 1 node
Design a Level 1a Network such that Topology is survivable (2-node connected) Edge capacities are sufficient (also in failure situations) Shortest path routing (OSPF) leads to balanced
capacity use (objective in network update) The whole network should be bdquostable for the futureldquo The overall cost should be as low as possible
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
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MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
59
Potential node locations for the 3-Level Network of the G-WIN
Red nodes are potentiallevel 1 nodes
CostConnection between nodesCapacity of the nodes
Blue nodes are all remaining nodes
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
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COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
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102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
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104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
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MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
60
Demand distribution
The demand scales with the height of each red line
AimSelect backbone nodes and
connect all non-backbone nodes to a backbone node
such that theoverall network cost is minimal
(access+backbone cost)
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MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
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MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
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COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
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COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
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COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
61
G-WiN Location Problem Data=set of locations
set of potential Level 1a locations (subset of ) set of possible configurations at
location in Level 1a
For and
connection costs from to
tr
==
isin isin isin
=
=
p
p
ip
i
VZ VK
p
i V p Z k Kw i pd affic demand at location
capacity of location in configuration
costs at location in configuration
1 if location is connected to (else 0)
1 if configuration is used at loc
=
=
=
=
kp
kp
ip
kp
ic p k
w p kx i p
z k ation (else 0)p
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
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MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
62
G-WiN LocationClustering Problem
min
1
1
isin isin isin isin
+
=
le
=
=
sumsum sum sum
sum
sum sum
sum
sum
p
k kip ip p p
p Z i V p Z k K
ipp
k ki ip p p
i kkp
kkp
p
w x w z
x
d x c z
z
z const
Each location i must be connected to a Level 1 node
Capacity at p must be large enough
Only one configuration at each Location 1 node
All variables are 01
of Level 1a nodes
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
63
Solution Hierarchy amp Backbone
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
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Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
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Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
64
G-WiN Location Problem Solution Statistics
The DFN problem leads to ~100000 01-variablesTypical computational experience
Optimal solution via CPLEX in a few seconds
A very related problem at Telekom Austria has~300000 01-variables plus some continuous variables
and capacity constraintsComputational experience (before problem specific fine tuning)
10 gap after 6 h of CPLEX computation60 gap after bdquosimplificationldquo (dropping certain capacities)
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
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MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
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MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
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MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
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MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
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MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
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COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
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Praumlsentationsnotizen
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MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
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MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
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MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
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MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
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MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
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120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
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Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
65
Contents1 How it began My Telecom Involvement Telecommunication The
General Problem2 The Problem Hierarchy Cell Phones and Mathematics3 The Problem Hierarchy Network Components and Math4 Network Design Tasks to be solved
Addressing Special Issues5 Frequency Assignment in GSM6 The UMTS Radio Interface7 Locating the Nodes of a Network 8 Balancing the Load of Signaling Transfer Points9 Integrated Topology Capacity and Routing Optimization as well as
Survivability Planning10 Planning IP Networks11 Optical Networks12 Summary and Future
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
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MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
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MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
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MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
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MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
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MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
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MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
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MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
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MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
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MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
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122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
66
Re-Optimization of Signaling Transfer Points
Telecommunication companies maintain a signaling network(in adition to their communication transport network) This is used for management tasks such as
Basic call setup or tear down
Wireless roaming
Mobile subscriber authentication
Call forwarding
Number display
SMS messages
etcA Eisenblaumltter A M C A Koster R Wallbaum R Wessaumlly Load Balancing in Signaling Transfer PointsZIB-Report 02-50
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
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MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
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MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
67
Signaling Transfer Point (STP)
CCD
CCD
CCD
CCD CCD
CCD
CCD
CCD
CCD
Link-Sets STP
Cluster
Cluster
Cluster
CCLK
CCD=Common Channel Distributors CCLK=Common Channel Link Controllers
CCD=routing unit CCLK=interface card
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
68
STP ndash Problem description
Target
Assign each link to a CCDCCLK
Constraints
At most 50 of the links in a linkset can be assigned to a single cluster
Number of CCLKs in a cluster is restricted
Objective
Balance load of CCDs
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
69
STP ndash Mathematical modelData
C set of CCDs j
L set of links i
Di demand of link i
P set of link-sets
Q set of clusters
Lp subset of links in link-set p
Cq subset of CCDs in cluster q
cq CCLKs in cluster q
Variables
01 isin isin isinijx i L j C1=ijx if and only if link i
is assigned to CCD j
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
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116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
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118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
70
STP ndash Mathematical model
2
min1
01
p q
q
ijj C
i iji L
i iji L
pij
i L j C
ij qi L j C
ij
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
isin
isin
isin
isin isin
isin isin
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
sum
sum
sum
sum sum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Min load difference
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
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87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
71
STP ndash former (unacceptable) solution
Minimum 186 Maximum 404 Load difference 218
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Loa
d
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
72
STP ndash bdquoOptimal solutionldquo
Minimum 280 Maximum 283 Load difference 3
050
100150200250300350400450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18CCD
Tra
ffic
Lo
ad
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
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95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
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97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
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98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
73
STP ndash Practical difficulty
Problem 311 rearrangements are necessary to migrate to the optimal solution
Reformulation with new objective
Find a best solution with a restricted number of changes
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
74
STP ndash Reformulated Model
( )
2
min1
01
p
p q
q
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
iji L j C j j i
L
y zx i L
D x y j C
D x z j C
x p P q Q
x c q Q
x
x B
isin
isin
isin
isin isin
isin isin
isin isin ne
minus
= isin
le isin
ge isin
le isin isin
le isin
isin
le
sum
sum
sum
sum sum
sumsum
sum sum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
Integrality
Restricted number of changes
Min load difference
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
75
STP ndash Alternative Model
( )
2
min
1
01
p
p q
q
iji L j C j j i
ijj C
i iji L
i iji L
iji L j C
ij qi L j C
ij
L
x
x i L
D x y j C
D x z j C
x p P q Q
x c q Q
xy z D
isin isin ne
isin
isin
isin
isin isin
isin isin
= isin
le isin
ge isin
le isin isin
le isin
isin
minus le
sum sum
sum
sum
sum
sumsum
sumsum
Assign each link
Upper bound of CCD-load
Diversification
Lower bound of CCD-load
CCLK-bound
IntegralityRestricted load difference
Min changes
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
76
STP ndash New Solutions
050
100150200250300350400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
CCD
Traf
fic L
oad
White D=50 (alternative)Minimum 257 Maximum 307
D=Load difference 50 Number of changes 12Orange B=8 (reformulated)
Minimum 249 Maximum 339 Load difference 90 Number of changes=B 8
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
77
STP ndash Experimental results
Max changes 0 5 10 15 20
Load differences 218 129 71 33 14
1 hour application of CPLEX MIP-Solver for each case
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
78
STP - Conclusions
It is possible to achieve85
of the optimal improvement with less than 5
of the changes necessary to obtain a load balance optimal solution
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
79
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
80
Network Optimization
Networks
Capacities Requirements
CostWessaumlly Roland DImensioning Survivable Capacitated NETworks PhD Thesis TU Berlin 2000 (awarded with the Mannesmann-Innovationspreis)
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
IP Routing Node Equipment Planning Optimizing Optical Links and Switches
DISCNET A Network Planning Tool(Dimensioning Survivable Capacitated NETworks)
atesio ZIB Spin-Off founded by A Eisenblaumltter and R Wessaumlly
speciallecture
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
82
Survivability-Modelstoday still a hot topic
H B
D
F
M
120H B
D
F
M
3030
60Diversificationbdquoroute node-disjointldquo
Path restorationbdquoreroute affected demandsldquo(or p of all affected demands)
6060
H B
D
FM
H B
D
FM
H B
D
FM
60
60
Reservationbdquoreroute all demandsldquo(or p of all demands)
120
H B
D
FM
H B
D
FM
H B
D
FM
60
60
mathematical models and software for
plus simultaneous capacity planning and routing
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Survivable Network Design Mathematical Model (example)
MartinGroumltschel
83
isin cap isin isin
minus
isin =
isin isin
isin
=
isin
isin isin =
ge isin =
= isin
ge isin
ge isin isin isin
+ ge
= isin
sum
sum
sum
sum
sum
sum sum
sum
0
0
0
0
0
0
1
0
1
01 1
1
( ) 0
m
( )
( )
( ) ( )
i
n
s su
e
v uv u
e
v
uv
uv
e uvu
s suv s uv
suv uv
v D P P e P
u
P P P P P e P
te e
t te e e
Tt t
e e et
Tt
v uv
t
P
e et
P
e E
f P s S uv D
y c
y f P e E
d f P uv D
x e E
x e E t T
x x e E t
k x
P Pf P f P
T
σ
isin isin cap isin isin isin
isin isin
+ le isin isinsum sum sum0
0
( ( ) ( )) s s
s uv uv uv
uv uv s
suv uv e s
uv D P P P e P P P e P
d s S uv D
f P f P y s S e E
topology decisison
capacity decisions
normal operation routing
component failure routing
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Network Planningdetails later today
MartinGroumltschel
84
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
85
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
86
DFN German Research NetworkInternet for German universities scientific institutions museums libraries etc
X-Win since 2006Bley Andreas Routing and Capacity Optimization for IP Networks
PhD Thesis TU Berlin 2007(awarded with the Dissertation Prize 2007 of the Gesellschaft fuumlr Operations Research and the INFORMS Doctoral Dissertation Award for Operations Research in Telecommunications 2008)
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
87
X-Win httpwwwdfndexwin Das Wissenschaftsnetz X-WiN
Maszliggeschneidert fuumlr Wissenschaft und Forschung
Das Wissenschaftsnetz X-WiN ist die technische Plattform des Deutschen Forschungsnetzes Uumlber das X-WiN sind Hochschulen Forschungseinrichtungen und forschungsnahe Unternehmen in Deutschland untereinander mit den Wissenschaftsnetzen in Europa und auf anderen Kontinenten verbunden Daruumlber hinaus verfuumlgt das X-WiN uumlber leistungsstarke Austauschpunkte mit dem allgemeinen Internet
Mit Anschlusskapazitaumlten bis zu 10 Gigabits und einem Terabit-Kernnetz das sich zwischen ca 60 Kernnetz-Standorten aufspannt zaumlhlt das X-WiN zu den leistungsfaumlhigsten Kommunikationsnetzen weltweit
Andreas Bley (ZIB now TU Berlin) has significantly contributed to the planning of the X-Win Locations
Network
Hub and Line Capacities
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
X-WIN G-WIN served the ~750 scientific institutions from
2000 to 2006
G-WIN was reconfigured about every two months to meet changes in demand Three modifications were allowed at each update at most
With new transport hub and switching technologies new design possibilities arise We have designed the new German science network called X-WIN which started operating at the end of 2006 (terabit backbone 10 gigabitsecond connectionshellip)
MartinGroumltschel
88
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
X-WIN
MartinGroumltschel
89
Node Bandwidths Level 1a and some 1b Nodes
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Data and a glimpse at the model
MartinGroumltschel
90
initial model 1 billion variablesafter reduction ~100000 variables ~100000 constraintssolved by ZIMPLCPLEXin a few minutes 81 scenarios have been
considered and solved ndashafter lots of trials ndash for eachchoice of reasonable number of core nodes
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Number of Nodes in the Core Network
MartinGroumltschel
91
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Location- and Network Topology Planing solvable to optimality in practice
GAR
ERL
BAY
MUE
FZJ
AAC BIR
DES
HAM
POTTUB
FZK
GSI
DUI
BRE
HAN
BRA MAGBIE
FRA
HEI
STU
REG
DRE
CHE
ZIB
ILM
KIE
ROS
LEI
JEN
ESF
HUB
ADH
KAI
GOEKAS
MAR
GIE
Faser KPN
Faser GL
Faser GC
Faser vorhanden
Wellenlaumlnge
GRE
Vorfuumlhrender
Praumlsentationsnotizen
Example 03 proven optimality gap for real 700 nodes network within lt 30 minutes13Knoten757 (davon 30 potentiell backbone)13Kanten 640713Demands 122180
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
X-Win Backbone January 2009
MartinGroumltschel
93
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
94
The network design problem
Supply Graph
Demands
Discrete Capacities amp Costs
OSPF-Routing
Survivability
Further technical constraints
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
95
OSPF-Routing Weights
Non-bifurcated routing on shortest pathswrt non-negative link weights
Sink-tree for each destination
Unique shortest paths necessaryto guarantee feasible routing in practice
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
96
OSPF-Routing Survivability
Survivability Capacities must accommodate a feasible OSPF-routing in
bull the normal operating state
bull single edge and single node failure states
2-node-connectivity
HH
H
L
B
K
F
Ka
SM
N
XXX
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
97
Model amp Solution approach
Mixed-integer programming model
Solution approach (Decomposition) Network design
Cutting plane algorithm
Heuristics
Weight computationLinear programming
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
98
Results Original network
Demands Nov 1997
Routing with perturbed unit-weights
Original topology
Cost 1204
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
99
Results New Network
Demands Nov 1997
Routing with perturbed unit-weights
Maximal 3 topology changes
Cost 1071
10 improvement on the network that has already
been optimizedwith our algorithm
HH
H
L
B
K
F
Ka
SM
N
Vorfuumlhrender
Praumlsentationsnotizen
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
100
ConclusionOSPF-routing (weights)
andtopology amp capacities
must be simultaneously optimized
Vorfuumlhrender
Praumlsentationsnotizen
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
X-WiN Traffic Engineering Results
Reduction of the maximal load to below 50 of the initial max load
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
102
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
103
Telecommunication networks
bull Focus Backbone layerbull Planning-objective Cost-minimal networkbull Reason New technology new services
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
104
From copper to fiberhellip
high transmission-capacity but restricted mileage
various types
(uni- and bi-directional)
various qualities
Electronic Networks
Edgeselectronic
Nodeselectronic
Fiber-Networks
Edgesoptic
Nodeselectronic
Fiber
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
105
hellipto WDM hellip
Capacity is multiplied
growing multiplex factors
different systems
(channels and spectra)
Fiber-Networks
Edges opticNodes electronic
Wavelength DivisionMultiplexing (WDM)
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
106
hellip to all optical networks
Switching optical channels wo o-e-o-conversion
Switching of arbitrary wavelengths
(Point-to-Point-) WDM-Networks
Edgesoptic (WDM)
Nodeselectronic
Optical Networks
Edgesoptic (WDM)
Nodesoptic
Optical devices
Optical Cross-connect (OXC)
Optical WavelengthConverter
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
107
Lightpaths
Lightpath = pure optical connection between twonodes via one or multiple fibers with opticalswitching in traversed nodes
length restriction (dispersion and attenuation)
wavelength assignment
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
108
Optical Network Configuration
physicaltopology
virtualtopology
lightpathconfiguration
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
109
Planning Optical Networks
DimensioningEdges Transmission-capacity
Nodes Switching-capacity
RoutingDetermination of routing
(with survivability)
ColoringConflict-free wavelength
assignment (with converters)
Planningpresent networks
Planningoptical networks
Input Network topology and demand-matrixOutput Cost-minimal network configuration with
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
110
Modeling Optical Networks Overall problem is too complex
extreme large mathematical model (intractable)
Decomposition into two subproblems Dimensioning and Routing
connection to previous network planning
integer routing requirement
Wavelength Assignment
conflict-free wavelength assignment to lightpaths
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
111
Dimensioning and RoutingPresent
Network Dimensioning and Routing
Capacity planning mainly edge capacities
rArr integer capacity variables
Routing either bifurcated (splittable) rArr continuous flow or path variables
or non-bifurcated (unsplittable)rArr 0-1 flow or path variables
Optical Network Dimensioning and Routing
Capacity planning both edge and node related
rArr integer capacity variables
Routing in lightpaths (integer-valued)rArr general integer routing variables
Lightpath length restrictionrArr only via path variables
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
112
Integer Programming Formulation
G =(VE ) Physical topology
Q Demand set (sqtqdq) source target and lightpath demand
P q Set of paths from sq to tq that are allowed to route lightpaths for commodity q
Tmn Index set of available edge capacity levels (fibers + WDM systems) for edge mn
κ0mn κt
mn Installed edge capacity (channels) available capacity levels
cTmn Cost of installing edge capacity level t at edge mn
Θm Index set of available node capacity levels (OXCs) for node m
κ0m κθm Installed node capacity (ports) available capacity levels
cθm Cost of installing node capacity level θ at node m
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
113
Integer Programming Formulation
of lightpaths of commodity routed via path
0-1 variable indicating whether edge capacity level is used at edge 0-1 variable indicating whether node capacity level is used at node
qp
tmn
θm
q pz
t mnx
θ
m
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
114
Integer Programming Formulation
0
0
0
min
1
1
01
m mn
q
qmn
mn
q qm
m
t tOXC m mn mn
m V mn E t T
q qp
p Pq t tp mn mn mn
q Q t Tp P mn ptmn
t T
q qp m m m
q Q p P m p q Q m s
m
q tp mn m
c x c
s t z d q Q
zκ κ mn E
mn E
z dκ κ x m V
x m V
z Z x
θ
θ
θ θ
θ
θ
θ
isin isinΘ isin isin
isin
isin isinisin isin
isin
isin isinΘisin isin isin =
isinΘ
+
+
= forall isin
le + forall isin
le forall isin
+ le + forall isin
le forall isin
isin isin
sum sum sum sum
sum
sum sum sum
sum
sum sum sum sum
sum
01θ isin
Routing
EdgeCapacity
NodeCapacity
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
115
Formulation Alternatives Depending on concrete capacity structure other variables
can be used
Every lightpath can be considered as a single commodity non-bifurcated routing of commodities all with unit demand
number of variables is blown up
available inequalities for non-bifurcated routing are lessnot effective for unit demands (with integer capacity)
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
116
Computational Experiments Deleting integrality requirements yields surprisingly few
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
Formulation alternative with dq non-bifurcated commodities unattractive
IP traffic results in assymmetric demand matrix symmetric routing not possible
asymmetric routing formulation
Multi-hop networks require 2-layer formulation
Wavelength assignment introduces a new aspect of optical network design
Survivability concepts have to be added
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
118
Contents1 How it began My Telecom Involvement2 Telecommunication The General Problem3 The Problem Hierarchy Cell Phones and Mathematics4 The Problem Hierarchy Network Components and Math5 Network Design Tasks to be solved
Addressing Special Issues6 Frequency Assignment in GSM7 The UMTS Radio Interface8 Locating the Nodes of a Network 9 Balancing the Load of Signaling Transfer Points10 Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning11 Planning IP Networks12 Optical Networks13 Summary and Future
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
119
Summary
Telecommunication Problems such as
Frequency Assignment Locating the Nodes of a Network Optimally Balancing the Load of Signaling Transfer Points Integrated Topology Capacity and Routing Optimization
as well as Survivability Planning Planning IP Networks Optical Network Design and many others
can be succesfully attacked with optimization techniques
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
120
SummaryThe mathematical programming approach
Helps understanding the problems arising Makes much faster and more reliable planning possible Allows considering variations and scenario analysis Allows the comparison of different technologies Yields feasible solutions Produces much cheaper solutions than traditional
planning techniques Helps evaluating the quality of a network
There is still a lot to be done eg for the really important problems optimal solutions are way out of reach
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
Integrating Variable Multimedia Services
Time of Day Usage PatternsCourtesy Dr Winter (E-Plus)
Vorfuumlhrender
Praumlsentationsnotizen
Various Multimedia Services13Die verschiedenen Multimediadienste in einer Anwendung in einem Dienst von einem Kunden Da muss noch sehr viel passieren
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
MartinGroumltschel
122
The Mathematical Challenges Finding the right ballance between
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
COW
The ATampT to atampt story
MartinGroumltschel
123
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
Martin Groumltschel Institut fuumlr Mathematik Technische Universitaumlt Berlin (TUB) DFG-Forschungszentrum bdquoMathematik fuumlr Schluumlsseltechnologienldquo (MATHEON) Konrad-Zuse-Zentrum fuumlr Informationstechnik Berlin (ZIB)
groetschelzibde httpwwwzibdegroetschel
Combinatorial Optimization in Telecommunication
COW Berlin
Martin Groumltschel
5 10 2009900 ndash 1030
The End
Vorfuumlhrender
Praumlsentationsnotizen
LP and IP current practice and some new theory1313Martin Groetschel13ZIB TU and Matheon Berlin1313Abstract1313In this talk I will give a brief survey about the development of13linear and integer programming in the last fifty years and would13like to show what the current state of the art in practical13problem solving in linear and integer programming is I will13report about experience at the Konrad-Zuse-Zentrum with the13solution of large-scale linear and integer programs coming from13practice to indicate the size of the problem instances that we13can successfully attack today1313I will also report about a new way to view linear programs as13semialgebraic sets There are some theoretical results a few13speculations but no algorithmic ideas yet1313 1313
Combinatorial Optimization in Telecommunication COW Berlin
Todayrsquos program
Contents
Contents
The beginning Clyde Monma (Bell LabsBell Communications Research)
TheBellCorestudy
The IP Model
Foliennummer 8
Foliennummer 9
Facets one example
Facets anotherexample
Recall The Importance of Facets
Recall The Importance of Facets
Real data
Problem reductions
Computational results with real data
LATA DL optimal solutions
Problem
But then USA 1987-1988(collected by Clyde Monma)
USA 1987-1988
Special Report by IEEE Spectrum
Special Report IEEE SpectrumJune1988
Not unfrequent in industry
Berlin 1994 amp Koumlln 1994
High-TechTerrorism 1995
Berlin 1997 amp Wien
OumlsterreichAustria
MediterraneanIceland
Most recent event in Germany (I know of)
Industry Partners
The ZIBMATHEON Telecom-Team
Contents
Advertisement
What is the Telecom Problem
What is the Telecom Problem
Contents
Cell Phones and Mathematics
Production and Mathematics Examples
Mobile Phone Production Line
Contents
Network Components
Component bdquoCablesldquo
Component bdquoAntennasldquo
Component bdquoBase Stationldquo
ComponentbdquoMobile Switching CenterldquoExample of an MSC Plan
Contents
Network Design Tasks to be solved Some Examples
Network Design Tasks to be solved Some Examples (continued)
Connecting Mobiles Whatacutes up
Contents
Frequency or Channel AssignmentRadio Interface
GSM Minimum InterferenceFrequency Assignment Problem (FAP)
GSM Region Berlin - Dresden
UMTS Configuration of Antennas
Optimization Reduction of UMTS Network Load
Contents
G-WiN Data
G-WiN Problem
Potential node locations for the 3-Level Network of the G-WIN
Demand distribution
G-WiN Location Problem Data
G-WiN LocationClustering Problem
Solution Hierarchy amp Backbone
G-WiN Location Problem Solution Statistics
Contents
Re-Optimization of Signaling Transfer Points
Signaling Transfer Point (STP)
STP ndash Problem description
STP ndash Mathematical model
STP ndash Mathematical model
STP ndash former (unacceptable) solution
STP ndash bdquoOptimal solutionldquo
STP ndash Practical difficulty
STP ndash Reformulated Model
STP ndash Alternative Model
STP ndash New Solutions
STP ndash Experimental results
STP - Conclusions
Contents
Network Optimization
What needs to be planned
Survivability-Modelstoday still a hot topic
Survivable Network Design Mathematical Model (example)
Network Planningdetails later today
Contents
DFN German Research Network
X-Win httpwwwdfndexwin
X-WIN
X-WIN
Data and a glimpse at the model
Number of Nodes in the Core Network
Location- and Network Topology Planing solvable to optimality in practice
X-Win Backbone January 2009
The network design problem
OSPF-Routing Weights
OSPF-Routing Survivability
Model amp Solution approach
Results Original network
Results New Network
Conclusion
X-WiN Traffic Engineering Results
Contents
Telecommunication networks
From copper to fiberhellip
hellipto WDM hellip
hellip to all optical networks
Lightpaths
Optical Network Configuration
Planning Optical Networks
Modeling Optical Networks
Dimensioning and Routing
Integer Programming Formulation
Integer Programming Formulation
Integer Programming Formulation
Formulation Alternatives
Computational Experiments
Concluding Remarks on Optical Networks
Contents
Summary
Summary
Foliennummer 121
The Mathematical Challenges
The ATampT to atampt story
Combinatorial Optimization in Telecommunication COW Berlin
