the “forcer” concept & forcer-clipping ring-mesh hybrid networks e e 681 - module 14 w.d....

The “Forcer” Concept The “Forcer” Concept & Forcer-Clipping Ring-Mesh Hybrid & Forcer-Clipping Ring-Mesh Hybrid

NetworksNetworks

E E 681 - Module 14

W.D. Grover

TRLabs & University of Alberta© Wayne D. Grover 2002, 2003

E E 681 - Module 14 © Wayne D. Grover 2002, 2003 2

• If AC is cut, 5 restoration paths exist on ABC and 5 on ADC.

• If AB is cut, 2 restoration paths exist on ACB and 5 on ADCB.– > AB ‘forces’ 7 spares on BC

• Similarly, Span AC is the forcer for spans AB, AD, and DC (5 spare links)

• Forcer threshold is the decrease needed (in the number of working links) to change a forcing span into a non-forcer (for AB that would be 3).

2(10, 2)

B

A C

D

(10, 2)

(2, 5)

(2, 7)

(3, 5)(7, 5)

5

B

A C

D

(2, 5)(2, 7)

(3, 5)(7, 5)

55

(working,spare)

B

A C

D

(10, 2)

(2, 5)(2, 7)

(3, 5)(7, 5)

Why does span BC have 7 spares in this design?

Introducing the “Forcer” Concept:

Forcer relationship


The Forcer Concept (by example)

13271,29,-27

174,53,46

753,74,32

6555,20,24

54

7

371,19,17

816,45,-29

453,0,-37

1248,27,1

968,14,-8

1316,41,16

8

1059,18,1

1481,0,-12

652,6,-32

1747,28,1

1841,16,41

11

9

10

1151,39,13 15

50,3,-37 1648,23,-3

1957,3,-30

2265,33,-14

2064,22,-4

2334,78,19

2178,34,53

2

Span Number

Working links, Spare links, Forcer Magnitude

Forcer Span

“Forcer Skeleton”

Network 1 - “Bellcore” (NJ LATA) - with published demand data - 11 nodes - 23 spans - Average degree = 4.2

Notes:

• Forcers are red

• Forcer magnitudes are the amount of wi by which the given span is above the threshold of being a forcer.

• Non-forcers has a negative forcer magnitude indicating how many wi additions are possible without requiring any increase in total network spare capacity.

“ All non-forcer spanscould have wi =0 and the total spare capacity for 100% span restorability would not be any lower.”

The forcer skeleton alone accounts for allthe spare capacity required in the optimal design.


Formal Statements

• Preamble:– In general, for any span j, there will always be some other span i,

which will require a number of spare links on j, that is equal to or greater than that required by any other failure span.

– When this relationship is true, we say that span i is the forcer (or a co-forcer) of span j.

• re: co-forcer: more than one span may require the same number of spares on span j, so the forcer relationships may be many-to-one.

• Definition:A forcer span is any span for which an increase in network total sparing is required to maintain restorability if the span's working capacity is increased. – Conversely, a non-forcer is a span on which at least one working

link may be added without requiring any additional spare capacity for the network to remain 100% restorable. “Super-restorability”


Algorithms for forcer analysis

1. Iterate the mesh spare capacity optimal solution:– idea is to observe change in as wi values are reduced.

• solve an initial mesh spare capacity placement (scp) problem

- for given set of wi

- record scp0 =

• for every span

- j:=0; spare_tot(j) := scp0

repeat

wi := wi -1 ; j:=j+1 ;

re-solve scp ;

spare_tot(j) < spare_tot(j-1) ?

if no, span i is a (now) a non-forcer; done_loop :=

true

if yes, span i is a (still) a forcer

until done_loop (and exit with j-1 as the “forcer strength” of span i)

spare

spare


2. Use a routing model of the restoration process:– idea is to discover which failures fully require the si values found on

other spans.

• solve an initial mesh spare capacity placement (scp) problem

• for every span x (taken as a failure span)

- run “ksp” as a simulation of the restoration process

- for every span i in the ksp pathset for failure x:

- record s i (x) - the number of spares on

span i

used upon failure of span x.

- if (s i (x) = s i ) then span x is a forcer of

span i.

- else (if s i (x) < s i then span x is not a

forcer of span i.)

until {done all spans, x} (and exit with the matrix of s i (x) values )

Algorithms for forcer analysis


Information encoded in the si (x) results

A. the logical forcer structure:

• for span i, every other span x such that (s i (x) = s i )…is a (co-) forcer of span i .

• for every span i, there must be at least one such other span x

Class: (or else what ...?)

• non-forcers are spans x such that s i (x) = s i is false for every i

B. measures of forcer magnitude: .... (next slide)

when span x fails .....

how much spare

does it use on span i ?

si (x) table

(x,i) where s i (x) = s i


( ) max ( ) max ( ) ,0,

i iF x s x s jij i x

x = a particular span, considered in its role as a possible forcer span

i, j = other spans of the network.

si (x) = amount of spare capacity used on span i, by restoration of span x.

Forcing Strength of span x on a specific other span i :

Measures of Global Forcer Strength of span x:

* max ( )( )F F xx ii x

{ }

* ( )( )i S x

F F xx i

Or...

Logical Forcer status of a span x

* 0( )* 0( )

F Forcer truex

F Forcer falsex

“ latent forcer ”

Measures of Forcer Magnitude encoded in the si (x) ...


Understanding the forcer magnitude and “latent forcer” relationships

Span x

Span j

Span i

Forces 14 sparesfor its restoration

Requires 10 spareson span i

for its restoration

( ) max ( ) max ( ) ,0,

max 14 10,0

4

i iF x s x s jij i x

Span jSpan k. . .

All other spansrequire < 10

spare on span i

max ( ) 10,

is jj i x

i.e. span j is the next latent forcer.

Aside from x itself, no other span requires

as much spare on ias does span j.

This D is the “forcer magnitude”

of x on i.


• Motivation:

– Hybrid designs may be lower in cost than pure ring or pure mesh.

• Pure ring designs typically contain some very inefficient individual rings

• Efficiency of pure mesh designs may be limited by dominant forcer effects ( demand-topology interactions, to be explained).

reference paper: W.D. Grover, R.G. Martens, “Forcer-Clipping: A Principle for Economic Design of Ring-Mesh Hybrid Transport Networks”, accepted (July 2000) for publication in Information Technology and Management, Special Issue on Design of Communication Networks.

An approach to ring - mesh hybrids based on the forcer analysis of mesh networks


DCS / OCX mesh

Termination costs

Network redundancy

Protection

- only dropped traffic needs terminations

ADM / OADM ringsTermination costs

Network redundancy

W

S1

S3

S2

W1 W2

W

DCS

DCS/OXC based $

RING MESH

ADM/OADM based$ Sparing high $

Sparing low $

W3

S

Why hybrids?: Comparing ADM-based rings and X-connect based mesh


Physical Topology

Logical Demand

Ring-2

Ring-1Ring-1

Selected “Forcer clipping” Rings

“ Residual Mesh”

ADM

Glassthrough

X-connect

hybrid transport

network

A first view of the hybrid concept being considered ...


• This is not a “multi-layer scheme” in the sense of involving fault

escalation.

• Every demand is protected on each segment of its route either in a

ring- or a mesh-survivability domain.

• Both ring and mesh components act simultaneously and

independently to protect demand segments in their domains

An important clarification…


The “forcer-clipping” hypothesis

• Preamble:– Measures such as F*(x) let us pinpoint which spans most drive the spare

capacity requirements of the surrounding restorable mesh network design. – F*(x) reflects the total 'height' by which span x's working link quantity is

above the point at which it would no longer be a forcer (i.e., other spans would become forcers, halting the relief of spare capacity)

• Main idea:– if the strongest forcers were removed or lowered, the complete mesh

network would become more efficient – maybe rings could be used to “clip off” these worst forcers ....

– hypothesis: a ring might be placed on the mesh network to 'clip the tops' off of one or more of the forcer spans, thereby more than proportionally reducing its total working and spare capacity cost.

• Net cost reductions would arise if the cost of the forcer-clipping ring is less than the net savings in the underlying mesh layer after its working capacity is adjusted and its spare capacity plan is re-optimized.


Self-contained BLSR “clips” off strong forcers

Reduces & levels underlying mesh

Residual mesh forcer landscape and “forcer-clipping” rings

Forcer span

spare capacity

Forcer span

‘hidden’ forcer

“forcer” landscape of a pure-mesh network

For certain ring placements, economies may arise from:

1) enhancement of the residual mesh capacity efficiency, due to forcer clipping

2) creation of a well-loaded ring, displacing wi quantities from the mesh, lowering relative termination costs.

The “Forcer Clipping” Hypothesis

• Rings could “clip the tops off ” strong forcers in the mesh, resulting in net savings, exceeding the cost of the rings.


A

F

G

Z

E

C

B(9,10)

(7,14)(16,14)

(10,10)

(16,0)

(9,10)

(14,20)

(14,20)

(29,16)

(30,15)

Pure mesh:

Redundancy = 129 / 154 = 0.84

(9,9)

(7,8)(16,8)

(10,9)

(16,3)

(9,10)

(2,9)

(2,9)

(17,10)

(18,9)

Test ring 1: Revised mesh:

Redundancy = 84 / 106 = 0.79

Capacity return ratio =

(129-84) + (154-106) 4 x 12 x 2

= 0.969

- just to see the nature of how ring and mesh interact in a capacity-design sense

- not yet guided by forcing clipping principle, but quantitatively exact mesh network redesigns following each ring trial placement

Example uses a 12 unit-capacity ring

Example of some actual ring-placement trials

“Capacity return ratio” = total (mesh working + re-designed sparing) reduction total (w + s) capacity represented by ring placement

High CRR --> good economics


A

F

G

Z

E

C

B(9,10)

(7,14)(16,14)

(10,10)

(16,0)

(9,10)

(14,20)

(14,20)

(29,16)

(30,15)

Pure mesh:

Redundancy = 129 / 154 = 0.84

(9,10)

(0,13)(4,3)

(10,10)

(16,0)

(9,10)

(14,20)

(14,20)

(17,17)

(30,14)

Test ring 2:Revised mesh:

Redundancy = 117 / 123 = 0.95

Capacity return ratio =

(129-117) + (154-123) 4 x 12 x 2

= 0.45

- just to see the nature of how ring and mesh interact in a capacity-design sense

- not yet guided by forcing clipping principle, but quantitatively exact mesh network redesigns following each ring trial placement

“Capacity return ratio” = total (mesh working + re-designed sparing) reduction total (w + s) capacity represented by ring placement

High CRR --> good economics

Example uses a 12 unit-capacity ring

Example of some actual ring-placement trials


- Heuristic 1: sums the global forcer magnitudes F*(x) of spans in the cycle

- Heuristic 2: looks at the fraction of logical forcersin the cycle, i.e.

Forcer analysis of initial mesh

Find all cycles of network graph

Use forcer assessments to build ranked “short-list” of ring placements

Place a “short-list” ring

Residual mesh re-design

Assess total economic impact

Callable CPLEX

Place max-payback ring and permanently alter the residual mesh design

Repeat until no further rings prove-in

no further gainfrom any ring

at least onering proves in

{ *( ) 0}

|{ } |x cycle

F x

x cycle

Heuristic Algorithms based on “Forcer Clipping”


Heuristic Algorithms: Details

1. The optimal spare capacity problem of the initial pure-mesh network is solved.

2. All elemental cycles of the network graph are generated.

3. Forcer analysis is done, and the forcer-clipping merit and ranking of each ring candidate is determined.

4. The top-ranked candidates (by the criteria of 3.) are stored in a working set.

5. Main loop: (until the economic return factor of the best ring is < 1)

a) Secondary loop: (until all the candidate rings in the working set have been tested)

1) Place candidate ring.

2) Create IP tableau for the modified mesh design.

3) Solve the relaxed IP problem with CPLEX.

4) Obtain the new spare capacity total from the solution.

5) Calculate the economic return factor (capacity return x mesh cost/ring cost where mesh cost = 1

and ring cost = economy of scale factor x cost factor).

6) Compare the ring with the best found so far (the first ring excluded), replace if better.

b) If the economic return factor for the best ring is 1, it is placed and the mesh permanently altered.


Step 1: Forcer Analysis Stage

Pure Mesh Reference

Spare Capacity: 625Working Capacity: 1252Total Capacity: 1877

13271,29,-27

174,53,46

753,74,32

6555,20,24

54

7

371,19,17

816,45,-29

453,0,-37

1248,27,1

968,14,-8

1316,41,16

8

1059,18,1

1481,0,-12

652,6,-32

1747,28,1

1841,16,41

11

9

10

1151,39,13 15

50,3,-37 1648,23,-3

1957,3,-30

2265,33,-14

2064,22,-4

2334,78,19

2178,34,53

2Span NumberWorking links, Spare links, Forcer Threshold

Forcer Span

Very weak forcers (F*(x)=1)

are ignored here

Example


Spare Capacity: 625 323

Working Capacity: 1252 730

Total Cost: 1877 1705

After 3 ring placement iterations

OC-48 BLSR (x3)

Ring Cost Factor = 0.8

Net Cost Reduction: 172 (9%)

Example (cont’d)


Residual Mesh Resultant

- lower spare capacities

- increased mesh efficiency13

223,9,-1

126,7,22

75,26,-2

657,24,-19

54

7

323,11,-22

816,17,2

453,1,-2

1248,1,-1

920,33,-23

130,0,0

8

1059,17,1

1481,0,15

652,4,1

170,25,-25

180,0,0

11

9

10

1151,15,-10 15

50,4,-24 1648,26,-4

1957,21,1

2217,25,-36

2064,14,19

230,30,-13

2130,13,30

2Span NumberWorking links, Spare links, Forcer Threshold

Forcer Span

Example (cont’d)


(for assessment of heuristic performance)

Minimize: cost of spare and working in mesh, plus costs of rings placed.

Subject To: 1) The mesh must be restorable: Yi = set of eligible rest routes for span i xip = restoration flow assigned to pth elig. route for restoration of span i.

2) The mesh working capacity is reduced by rings: R = set of all cycles of graph

3) Restoration sparing for the residual mesh: Zi j = { Yi : route contains span j }

4) Ring capacity is modular (M modularities): bq is the working capacity offered by the qth modular ring size.

1 1

[ ] [ ]( )S M

q qmri i

i r R q

i rc s w c

1, ,i

i p ip Y

x w i S

0, i r i i

r R

w B w i S

;ji

ip k ip Z

x s i S k V

1..

; [ ]

qri q r

q M

B b

r R i S r

An Optimal Formulation

Reference: W. Grover, R. Martens, "Optimized design of ring-mesh hybrid networks,” Proc. DRCN 2000.


12, 24, 48-unit module ring capacities

{2cost4capacity} economy-of-scale model for rings

4-fibre BLSR ring capacity model

ADM-ring cost / unit installed capacity = mesh * cost factor @ 24 - unit modular capacity (see next slide)

‘gravity type’ point-to-point demand patterns

Other Data for Results:


“Cost factor” is defined asrelative cost per physical unit capacityto average DCS-terminated unit capacity in mesh for OC-24 ring

relative cost scale: ring / mesh

1.0

0.8

Mesh (per unit capacity)Rings (modular atsizes 12, 24, 48)

OC-12

OC-24

OC-48

May apply economy of

scale rule, e.g.,4 times

capacity for 2 times cost

Example:

• Cost factor = 0.8 implies that an OC-24 ring span (actually representing 48 units of capacity) is cost -equivalent to 0.8 (48) = 38.4 units of capacity on a mesh span

• Ring relative cost then scales up or down according to the economy of scale model employed

Ring-Mesh Relative Costing Model


Ring cost factor = 0.8

Objective function values, (% savings), execution time,number of rings

“Cost savings” arerelative to objectivefunction value for

“pure-mesh”

Network #1

11 nodes

23 spans

Network #2

11 nodes

20 spans

Network #3

15 nodes

28 spans

Average cost

savings %

Initial Mesh

(reference case)1877 1705 2211

Heuristic #1

1750 (6.8 %)

7.3 min

1 ring

1504 (11.8%)

1.7 min

1 ring

2092 (5.4 %)

50.8 min

1 ring

8.0

Heuristic #2

1705 (9.2 %)

20.1 min

3 rings

1509 (11.5 %)

2.1 min

1 ring

2092 (5.4 %)

38.4 min

1 ring

8.7

Optimal Solution

Method

1667 (11.2 %)

36.9 min

4 rings

1487 (12.8 %)

6.3 min

3 rings

2088 (5.6 %)

25.3 hrs

4 rings

9.9

LP Lower Bound 1617 1437 1888

*

* result obtained with MIPGAP = 200

Some Results( … where optimal and heuristic can be compared)


Ring cost factor = 0.6

Objection function values (total cost), execution times, and number of rings placed

Network #1

11 nodes

23 spans

Network #2

11 nodes

20 spans

Network #3

15 nodes

28 spans

Average

cost

Savings %

Initial Mesh

(reference case)1877 1705 2211

Heuristic #1

1589 (15.3 %)

10.5 min

2 rings

1350 (20.8 %)

2.5 min

2 rings

1913 (13.5 %)

2.1 hrs

3 rings

16.5

Heuristic #2

1507 (19.7 %)

20.9 min

4 rings

1373 (19.5 %)

2.1 min

1 ring

1740 (21.3 %)

4.4 hrs

4 rings

20.2

Optimal Solution

Method

1411 (24.8 %)

10.9 hrs

5 rings

1275 (25.2 %)

31.2 min

5 rings

1873* (15.3 %)

23.3 hrs

8 rings

21.8

LP Lower Bound 1311 1175 1473

* result from optimal formulation after 24

hours

Some Results( … where optimal and heuristic can be compared)


Heuristic

#2

% savings over optimal pure mesh

Number of rings placed

CPU time

Net #4

19 nodes

39 spans

Net #5

16 nodes

29 spans

Net #6

27 nodes

48 spans

23.8%

8 rings

11.9 hrs

38.6%

12 rings

1.0 hr

39.5%

11 rings

2.3 hrs

Other Results (where only the heuristic can go):


But if rings are less costly, won’t the solution just slide to an all-rings design ?No: There is a true Cross-Architectural Optimum design point

Network #1, Heuristic #2

Ring Cost Factor = 0.8

Combined Cost of Rings and Mesh

1600

1650

1700

1750

1800

1850

1900

0 1 2 3 4

Number of Rings Used

Co

st

Test case where heuristic was compelledto place one more ring (4) than it wanted.

Question


Insights - understanding hybrid and why it “works”

• A good forcer clipping ring pays for itself by: • (1) attaining good utilization for itself, while displacing mesh capacity

• (2) enhancing the mesh efficiency through forcer-levelling.

• But even when ring transport is up to 40% cheaper than mesh,

architectural aspects lead to a hybrid - not a pure ring outcome. -

why? • Pure ring or pure mesh now seen to arise only as limiting cases:

– (1) “rings must be rings” …closing the circle limits ring efficiency.

– (2) mesh residual become more and more efficient (because it becomes

more forcer leveled) and eventually no ring addition can pay off anymore

• Why is the prediction of “forcer levelling” in the residual meshes

not more evident in the results than actually seen?

• When rings are placed they scour out mesh capacity to their full depth,

not just the forcer peaks they were placed to ‘clip’.


• The “forcer-clipping” hypothesis is suggested as an effective principle in ring-mesh hybrid network design.

• Advent of DCS with integrated ADM shelf functionality motivates / enables this type of true hybrid.

• Heuristics observed to be within ~ 5% of optimal for test cases– This is taken as confirming the basic validation of the forcer-clipping insight.

• Heuristic #2 seems superior, and executes in reasonable time for large problems

– Heuristic 2 thought to be “selecting in” more co-forcer and latent-forcer combinations which the economic trial placements then discover and exploit

• This work suggests that in general even mesh networks should be examined for “express ring” opportunities.

Summary of Main Findings

the “forcer” concept & forcer-clipping ring-mesh hybrid networks e e 681 - module 14 w.d....

Documents