cnit italian national consortium for telecommunicationsqos.pdf · italian national consortium for...

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Control Techniques for Quality of ServiceGuarantees in Multiservice

Telecommunication Networks

Italian National Consortium for Telecommunicationscnit

Franco Davoli, Riccardo MinciardiDepartment of Communications, Computer and

Systems Science, University of Genoa, Italy

CNIT-University of Genoa Research [email protected], [email protected]

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Outline

Control problems in TelecommunicationNetworks General aspects and common ground Problem areas in networking control Heterogeneous networking environments Timescales - control, management, planning

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Outline (cont’d)

Call Admission Control, Bandwidth Allocationand Routing, Congestion Control Admission policies Service separation - Decoupling low- and high-level

constraints Bandwidth allocation in ATM and IP terrestrial, mobile

wireless and satellite networks - Dynamic routing of flows Scheduling Pricing

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Outline (cont’d)

Instances of control techniques in specificenvironments Access networks Mobile wireless networks and satellite networks Cross-layer approaches Approximation techniques and parametric

optimization

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Introduction

A large number of dynamic control and resourceallocation problems arise in almost all types ofcommunication networks.

Among others, some examples of the mostcommonly found ones are: Connection Admission Control (CAC) Bandwidth Allocation Congestion Control Routing Scheduling Power control in wireless networks

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Introduction (cont’d)

Such problems are encountered in differentnetworking environments, cabled and wireless;basicallyTDM-based structures (circuit-switched telephone

networks; mobile radio networks, even in conjunctionwith CDMA; satellite networks)

ATM networksIP networks with DiffServ/IntServ paradigms, MPLSOptical networks (with MPλS, GMPLS)Wireless networks

The various structures may appear together (inparticular, IP-over-X)

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Introduction (cont’d)

Control problems appear at various architectural layers Physical and Data Link: dynamic power control and fade

countermeasures, bandwidth allocation among users and services,multiple access, …

Network: dynamic bandwidth allocation, routing, Call AdmissionControl, packet scheduling, …

Transport: elastic bandwidth allocation, congestion control, … Application: congestion control (e.g., TCP-friendly applications),

rate adaptation, pricing, …

Cross-layer approaches (i.e., exploiting information fromother layers for control purposes) are often advisable,especially at lower layers in noisy environments.

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Purpose of the Course

To give an overview of some controlissues and techniques commonly usedin telecommunication networks

To show instances of their application indifferent networking environments

To point out possible open problemsand research areas

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Goals of control

The ultimate goal is to provide some level ofQuality of Service (QoS) to the entities (dataunits, connections, applications, end users)that are being considered, depending on thespecific layer or the “granularity” (or on thescope or “width”) they are looked upon.

According to ITU-T E800, QoS is interpretedasThe overall effect of performance-enabling

services that determine the degree of satisfactionof a service user.

From the viewpoint of the telecommunicationnetwork, QoS translates into the capability of thenetwork to guarantee a specific service level.

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Quality of Service

Indeed, the term QoS has a number ofinterpretations, which range from the qualityperceived by the service user to a set of performance(in general, layer-specific) parameters that isnecessary to specify to obtain the desired level ofservice.

E.g., one may distinguish– Intrinsic QoS : directly provided by the network and described in

terms of objective indicators, like loss (of data units or connections)and transfer delay.

– Perceived QoS - P-QoS: as subjectively measured by the MeanOpinion Score (MOS).

– Assessed QoS : as referred to the user’s willingness to continueusing a service. Related to P-QoS, but also dependent from thepricing mechanism, the support guaranteed by the provider andother commercial and market aspects.

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Service Level Specification

QoS provisioning is often offered in terms ofobjective indicators, by using aService Level Specification - SLS.

The SLS is a set of performance indexes andof their required values that together definethe service offered to a given traffic.

The SLS is the technical part of anagreement, negotiated between service userand provider, relatively to the characteristicsof the service itself and to the associated setof metrics (Service Level Agreement - SLA).

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Applications

Which applications need some form of QoS? All applications requiring a specified level of

“guarantee” from the network– Services for the transport of aggregate

information (bandwidth from providers, VPN) In the access network In the backbone network

– Videoconferencing, videotelephony– VoIP, Internet Telephony– Tele-medicine– Tele-education– Remote Control– Emergency (Disaster Recovery) applications– …

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Requests for QoS

Market requests Widespread diffusion of the Internet

Protocol Suite as a “universal” platform Need of mechanisms to provide quality

end-to-end QoS on IP networks andacross multiple domains.

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ITU-T QoS Classes (for IP)

Traditional applications of best-effort IP networks5

Low loss (short transactions, streaming data flow)4Data transactions, interactive3

Data transactions, highly interactive2Real-time, delay jitter sensitive, interactive1

Real-time, delay jitter sensitive, highly interactive0

CharacteristicsQoSClass

ITU-T Y-1541

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QoS metrics (IP)

IPLR - IP Packet Loss Rate IPTD - IP Packet Transfer Delay IPDV - IP Packet Delay Variation IPER – IP Packet Error Rate Skew (average value of the delay

difference among packets belonging todifferent, mutually synchronized, media)

…

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QoS metrics - Requirements

1 x 10-4Upper limitIPER

Un-specified

1 x 10-31 x 10-31 x 10-31 x 10-31 x 10-3Upper limit onpacket loss rate

IPLR

Un-specified

Un-specified

Un-specified

Un-specified

50 ms50 msUpper limit on1-10-3 quantile of

IPTD less minIPTD

IPDV

Un-specified

1 s400 ms100 ms400 ms100 msUpper limit onaverage IPTD

IPTD

Class 5Un-

specified

43210PerformanceParameter

QoS Classes

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QoS metrics - An example

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QoS control

Functionalities and Tools

Identification of traffic flows Call Admission Control Traffic Engineering Scheduling (Service discipline) Flow and congestion control QoS Routing Resource Allocation

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QoS control - Time scales

A wide range of time scales, with orders of magnitude fromfew µs to minutes, hours and days. Accordingly, a set of(related) resource allocation and control problems, spanning• Network Control• Network Management• Network Planning

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QoS mapping

Services offered by lower layers shouldprovide QoS mapping functions for thebenefit of higher layers

Implementing end-to-end guarantees (if at allpossible!) would imply cooperation amonglayers

However, care should be taken in cross-layerapproaches, in order not to disruptarchitectural principles that ensureinteroperabilty

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Transport technologies

Higher layers - IP

SONET/SDH(ATM)

TDM

Ethernet Other…

WDM

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QoS control - Technologies

“Throwing bandwidth at the problem”ATMIP (IPv4 and IPv6)

DiffServ / IntServ

MPLS

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Technologies - ATM

octects

octects

Traffic Flow Identification

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Technologies - ATM

Originated as QoS-oriented technology Statistical multiplexing with resource

reservation to guarantee service level Defined traffic parameters and

descriptors for QoS Too complex in terms of control plane,

signaling required, adaptation layers.

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Technologies - IP IntServ

Defines flows Signaling (RSVP) Guaranteed Service (GS)

– Reliable upper limit on source-destinationpacket delay

Controlled Load Service (CLS)– Comparable to best-effort in lightly loaded

network Hardly scalable

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Technologies - IP IntServ - RSVP

RSVP protocol– Activates connection upon request by source host– Does not require message for resource release– Requires (periodic) refresh messages to inform nodes traversed by a

connection that the connection is still active (soft state)– Connection is released only if refresh message times out

Advantages– Bandwidth guarantees

Disadvantages– Upon ternimation of IP flow, bandwidth not immediately released– Part of bandwidth used by “keep alive” signaling

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Technologies - IP DiffServ

Use of DSCP (DiffServ Code Point) –ToS – 8 bit (6 DSCP+2) in IP header

Traffic aggregation Scalability

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Three priority classes– Expedited Forwarding (EF) characterized by configurable

minimum service rate, independently of other aggregateswithin router; oriented to low delay and loss services

– Assured Forwarding (AF) specified for four independentclasses (AF1, AF2, AF3, AF4), though the number couldbe higher. Within each class traffic is differentiated in 3categories (drop precedence)

– Best Effort (BE) with no performance guarantee and QoSlevel

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Aggregate traffic handling

Control functionsMarkingClassificationRate control - Policing

Modular architecture:DiffServ domain (set of nodes)DiffServ region (set of contiguous domains)DiffServ network (set of regions)

Aggregate

Aggregate

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An example of DSCP assignment

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Technologies - IPv6

Version Traffic Class Flow Label

Payload Length Next Header Hop Limit

Source Address

Destination Address

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 11 2 3

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Technologies - IPv6

Version Class Flow Label

Payload Length Next Header Hop Limit

Source Address

Destination Address

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 11 2 3

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Technologies - MPLS

Label Switching - Traffic engineering capabilities

IP ATMMPLS QoS handling

Control functionsSimpleUniversally widespread

C1

C3

C2IP

IP 5IP 10

IP

LER

LSR

LERLSRLSR

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Technologies - MPLS

32-bits

Label MPLS

Label (20 bits) TTLSEXP

IP

– Label– Experimental– Stacking bit (indicates presence of more labels)– Time to live

IP on guaranteed performance network

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Technologies - MPLS

C1

C3

C2IP

IP 5IP 10

IP

LER

LSR

LERLSRLSR

– LER (Label Edge Router) at ingress applies Label to packet and sendsover correct LSP (Label Switched Path).

– LSRs (Label Switched Router) switch packet, swapping labels– Egress LER eliminates label and forwards packet with IP forwarding

procedure

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Technologies - Flow ID

ATM

IPv4

IPv6

Version Type of Service Total Length

Identification Flags Fragment Offset

Source Address

Destination Address

IHL

Time To Live Protocol Header checksum

Options Padding

TCP/UDP Port - Sourcee TCP/UDP Port - Destination

Version Class Flow LabelPayload Length Next Header Hop Limit

Source Address

Destination Address

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QoS control functions

Traffic flow identificationCACRate control, traffic shaping and filteringBandwidth allocation

Scheduling (service discipline)Flow and congestion controlQoS Routing

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QoS architectures - End-to-end example

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References

H.J. Chao, X. Guo, Quality of Service Control in High-Speed Networks,Wiley, New York, NY, 2002.

J. Walrand, P. Varaiya, High-Performance Communication Networks,2nd Ed., Morgan-Kaufmann, San Francisco, CA, 2000.

J. Kurose, K. Ross, Computer Networking, 3rd Ed., Addison-Wesley,Boston, MA, 2004.

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Control of TDM, ATM and IP networks

Time Division Multiplexing (TDM) networks still form a broadclass of existing systems, for which control methods havebeen developed and applied over the years. They stillconstitute the basis of a large amount of “legacy” circuit-switched networks (i.e., the telephone network), of a largenumber of satellite systems, of second generation cellularsystems (and also appear in 3rd generation ones, inconjunction with CDMA).

There is also another motivation to study some of themethods that are applicable in this context. Actually, manyconcepts developed therein refer to the notion of a“connection”, implying the allocation of a resource of somekind (e.g., bandwidth) over a considerably “long” time scale(with respect to, e.g., a time slot) and can be applied indifferent settings, by somehow decoupling control problemsat widely different time scales.

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Control of TDM, ATM and IP networks (cont’d)

In general, multiservice networks are encountered,i.e., networks where multiple classes of services,possibly characterized by different transmissionspeeds or statistical characteristics of their sources,or by specific performance requirements, are present.However, some techniques may also make sense in asingle service environment (e.g., trunk reservation incircuit-switched networks).

The stochastic knapsack model and product form lossnetworks, which are a basis for the study ofmultiservice loss systems (see, e.g., the book byK.W. Ross), are useful tools in this context.

Many teletraffic engineering concepts developed herecarry over to MPLS.

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Control of TDM, ATM and IP networks (cont’d)

As regards recalling some control techniques in theAsynchronous Transfer Mode (ATM), there is a similarmotivation. There is today a large basis of deployed ATMnetworks in the transport and access area, control techniques at“connection level” extend from the circuit-switched world to theATM environment, and some concepts may be further extendedto multiservice IP networks, which are the main focus of currentresearch activity.

Moreover, CAC and bandwidth allocation for guaranteedperformance (GP) flows (or a mix of them and best-efforttraffic) still are at the basis of current problem areas in thewireless environment.

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Control of TDM, ATM and IP Networks (cont’d)

Examples

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Examples

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Control of TDM and ATM Networks (cont’d)

Examples

(See, e.g., DVB-S and DVB-RCS Data Link Layer QoS classes)

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Examples

Similar structures in the access area also apply (withobvious modifications and interesting cross-layerinteractions arising) in wideband fixed wireless access (IEEE 802.16 and ETSI TR

102 003 standards, among others) in bandwidth allocation and admission control in the

interaction between base station and mobile terminals incellular radio networks (GSM, GPRS, UMTS)

in multiservice WLANs (based on IEEE 802.11, Bluetooth, …)

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Examples - Heterogeneity

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Examples

Data-link / Physical Layer Integration of Guaranteed Performance (bandwidth) and best-effort traffic

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Examples

Hierarchical Admission Control and Bandwidth Allocation

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Call-level Models, CAC and Routing

The stochastic knapsack model Blocking probability Call Admission Control Admission policies Optimal Complete Partitioning Knapsack models for ATM and IP Service Separation Routing Product Form Loss Networks

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The Stochastic Knapsack Model

Consider a pure loss queueing system, i.e., onewhere arriving objects are admitted (for the durationof their holding time) if there is room and blockedotherwise. A system of this kind where objects ofdifferent size ( ) arrive and departdynamically, according to some statisticaldistribution, is called a stochastic knapsack.

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The Stochastic Knapsack Model (cont’d)

The knapsack admits an arriving class-k object if

otherwise, the object is blocked and lost. Let be the number of class-k objects in the

knapsack at time t. Moreover, assume Poissonarrivals and exponential holding times (the model canbe generalized). The stochastic process ,where , is an aperiodic andirreducible Markov chain over the (finite) state space

N being the set of non-negative integers.

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Let be the stationary distribution, and be the offered load of class k. Then

i.e., the equilibrium probabilities have a Product Form. It is worth noting that the PF Solution holds for general

distribution of the holding times (insensitivity property).

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Blocking probability and throughput

Let be the set of non-blocking states for a class-k object.

Then the blocking probability of a class-k object is

The class-k throughput is

There are computational algorithms for an efficientcalculation of these quantities (see the book by K.W.Ross).

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The Generalized Stochastic Knapsack

In the basic knapsack model, λk(n)=λk, µk(n)=nkµk. In the moregeneral case of state-dependent arrival and departure rates,define

A necessary and sufficient condition for reversibility can begiven, which also characterizes the stationary distribution. Thelatter has not necessarily a PFS.

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Call Admission Control (CAC)

Admission control can be exerted in the presence ofmultiple services, in order to improve resourceutilization, enforce some degree of fairness, ormaximize revenue.

Optimal policies for the stochastic knapsack may beobtained, once defined the appropriate cost orrevenue function, by applying numerical methods forMDP’s.

However, the computational effort required by thesetechniques may be large, and considering someparticular types of policies (Coordinate Convex,Complete Sharing, Complete Partitioning, Threshold,Trunk Reservation, …) may restrict the search space.

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CAC (cont’d)

Admission policies

Consider a generalized stochastic knapsack, with statedependent arrival and departure rates, of the type

(note thatfor the pure loss system). Assume , which ensures the existenceof one ergodic class.

A (pure) admission policy is a mapping

Let be the set of recurrent states of thecontrolled Markov chain.(where is the vector of all 0’s, but for a 1 in the k-th position)

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CAC (cont’d)

Admission policies

In general, when the knapsack is operated under theadmission policy f, the equilibrium probabilities πf(n)can be derived from the global balance equations

( ), whosesolution can become computationally expensive forlarge C and K.

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CAC (cont’d)

Admission policies

We consider the following policiesComplete sharing (CS):

(for which S(f)=S)

Trunk reservation:

which admits a class-k object iff at least tk resourceunits would remain after admission.

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CAC (cont’d)

Admission policiesn2

n1

1

2

3

4

0 1

2

3 4

Trunk Reservation,C=4, K=2, b1= b2=1,

t1=0, t2=2

TR is not Coordinate Convex (CC). In CC policies, transitions always comein pairs.

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CAC (cont’d)

Admission policies

Note that all transitions in the diagram corresponding to acoordinate convex policy come in pairs. Coordinate convexpolicies are appealing, because they are characterized by aProduct Form stationary probability. Not all policies areCoordinate Convex (e.g., Trunk Reservation is not). CS iscoordinate convex (with associated set S) and so are thepolicies to be considered in the following.

Coordinate convex (CC): f is coordinate convex if∃ a coordinate convex set Ω⊆S s.t.

The set Ω is coordinate convex if

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CAC (cont’d)

Admission policies

The equilibrium probabilities of a coordinate convexpolicy are given by

with

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CAC (cont’d)

Admission policiesComplete Partitioning (CP): given K positive integers C1,…,CK, s.t. C1+ … + CK≤ C, a class-k object is admitted whenthe knapsack is in state n iff

so that the knapsack is decomposed into K smaller ones,each dedicated to a single class. CP is coordinate convex,with associated “rectangular” set

Since the classes are separated and do not interact, thestationary distribution has a product form, with the marginaldistribution πk(n) given by that of a birth-death process withrates and µk(n), namely:

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CAC (cont’d)

Admission policies

i.e., classes in Kj are assigned exclusively Cj resource units,and compete for them in complete sharing. CP and CS arespecial cases of partitioning.

Partitioning: given a partition K1,…,KL of K={1,…,K}(K1,…,KL are disjoint sets that cover all K), and L integersC1,…,CL, s.t. C1+…+CL≤C

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CAC (cont’d)

Admission policies

Threshold: given a set of positive integersC1,…,CK a threshold policy admits a class-kobject when in state n iff

(it is not required that the sum of the Cj’s be ≤C). The associated coordinate convex set is

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CAC-Admission policies (cont’d)

Revenue optimization

Consider a revenue function r(n), associated with staten. The long-run average revenue associated withpolicy f is given by

Just to give some examples, if the system is a pure loss one (i.e.,µk(n)=nµk , ∀k) and a class-k object in the knapsack generatesrevenue at rate rk, then

: if rk=bk, R(f) is the long-run average utilization; if

rk=µk, R(f) is the long-run average throughput.

For a memory-sharing system (one server dedicated to each classand a common buffer), if rk is the revenue rate when the k-thserver is active, then

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Revenue optimization

In the case of the pure loss system, the optimal policy may varyfrom the case of complete sharing (for arrival rates approachingzero) to complete partitioning (for arrival rates approachinginfinity, where the resulting deterministic knapsack problem maybe solved by using Dynamic Programming; in this case, if k* isthe class with highest per unit revenue (rk/bk), and C/bk* is aninteger, then k* completely hogs the system).

In general, the optimal policy is not coordinate convex (e.g., ifK=2, b1=b2=1 and r2>r1, a trunk reservation policy of the typef2(n)=1, f1(n)=1(C-n1-n2-t*), for some integer t*, is indeedoptimal).

Several interesting results exist for the characterization ofoptimal coordinate convex policies, especially in the cases of 2and 3 classes.

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Optimal Complete Partitioning

If the revenue function is separable

then the optimal complete partitioning policy can be foundby applying DP. In fact, for any given C1,…CK,

where πk(n) is the distribution of a birth-death process,and the allocation problem is

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Optimal Complete Partitioning

Let hk(D) be the maximum revenue accrued by classes 1through k with D resource units available. Then we havethe following DP algorithm

and subsequent optimal allocation

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CAC

Knapsack Models for ATM and IP

Consider a cell (or packet) multiplexer, whose basicelements are a finite buffer that stores cells (orvariable length packets) and a high-speed link withslotted timing. Virtual Channels (VC) connectionrequests (or flow requests in IP or MPLS), which weassume to be generated by bursty sources (individualor aggregate) of K different classes (services), withpeak-rates b1,…,bK, can be modeled, at theconnection level, exactly as circuit-switched calls.Therefore, the stochastic knapsack can modelconnection-level performance (of inelastic traffic).However, we need to distinguish the interaction withcell-level or packet-level performance, in order to,essentially, decouple two phenomena happening atwidely different (a few orders of magnitude) timescales.

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CAC


Though ATM is becoming “less fashionable”, thereare a number of reasons to consider cell-multiplexingproblems and cell-level QoS: In some networking environments, IP packets need to be

fragmented at layer 2 into smaller, fixed-size data units. Thisis the case of time-division (or time-code-division)multiplexing in radio networks and DVB (Digital VideoBroadcasting)-IP standards in satellite networks.

Concepts originally developed in the ATM world to decouplecall- and cell-level problems, like the equivalent bandwidthone, also apply, with slight modifications, to variable lengthIP packets.

Since ATM (and DVB) are still widely applied in sometransport networks, the problem of QoS mapping betweenthe IP layer and such other techniques is a relevant one.

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CAC (cont’d)


At the cell level, the buffer needs to absorbe cell-scale and burst-scale congestion. The former iscaused by simultaneous (i.e., in the same time slot)multiple cell arrivals, and requires a small buffer; thelatter occurs when the aggregated cell arrival rate,generated by all active VCs (flows), is temporarilygreater than the link capacity, and may require alarge buffer to be kept below a given limit (which, onthe other hand, may introduce a large delay).

Cell-level Quality of Service (QoS) requirements areusually specified in terms of cell loss probability (orrate) and of the probability (or rate) of exceeding aspecified delay bound.

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CAC (cont’d)


In another respect, one may be concerned with cell-scale models, based on the multiplexing of manysources (many-sources asymptotics) and with burst-scale models, based on buffering (large bufferasymptotics). These allow to determine the minimalbandwidth needed to satisfy given cell-loss (orpacket-loss) requirements.

Assume to be able to determine at least some subset(which may depend on the scheduling policy) of theset Λ of all allowable VC-profiles, i.e., of the K-tuplesn=[n1,…,nK], with nk representing the number ofconnected class-k VCs, which would satisfy cell-levelrequirements when permanently connected.

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CAC- Knapsack Models for ATM (cont’d)

Peak-Rate Admission

Under peak-rate admission, a new class-k VC isadmitted iff

so that the state space (possible VC profiles) is

Cell-level requirements are obviously always satisfied. Optimal admission policies may be derived over this

set, e.g., in order to maximize link utilization(r(n)=b.n) or minimize blocking, and either linearprogramming or value iteration techniques can beused to find them.

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CAC- Knapsack Models for ATM (cont’d)

Statistical Multiplexing

Now we allow VC profiles s.t.

However, the admission region S(f) under policy fmust be s.t. S(f) ⊆ Λ, i.e., cell-level requirements aresatisfied.

There are several possibilities. Optimizing over theset of all allowable VC-profiles (i.e., setting S=Λ)seems appealing, but Λ may be very difficult, if notimpossible, to determine. As multiplexing acrossservices with widely different cell-level requirementsor statistical characteristics of the sources yields littlegain in most cases, Service Separation may be aviable alternative.

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CAC- Knapsack Models for ATM and IP flows (cont’d)

Service Separation

Under Service Separation, statistical multiplexingtakes place among VCs of the same class (service),but not across different classes, which are assignedbandwidth partitions, by means of some schedulingalgorithm (e.g., Weighted Round-Robin, GPS, orother). Each class (service) has a dedicated buffer,served by the scheduler. IP DiffServ classes arebased on a similar concept.

1

K-1

K

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CAC- Knapsack Models for ATM and IP flows (cont’d)

Service Separation

Let βk(n) be the minimum capacity that is required tosatisfy cell-level QoS requirements for n permanentclass-k VCs multiplexed in a buffer of given capacityQ. This service-k capacity function depends on asingle type of homogeneous sources, and may befairly easier to determine, by analytical models orsimulation, than a similar quantity when multipleservices are involved.

If the k-th service can be assigned an effectivebandwidth , then the admissionpolicy could be the same as the peak-rate one, with substituting bk.

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CAC- Service Separation (cont’d)

Static Partitions

Let C1,…,CK, with C1+…+CK=C be a partition of thecapacity. Under Service Separation with StaticPartitions, an arriving class-k VC is admitted iff

The maximum number of class-k VCs in the system isgiven by

and the class-k blocking probability is given by theErlang-B loss formula.

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Dynamic Partitions

The scheduling weights are now proportional to β1(n1),…,βK(nK), so that they are changing, but on amuch longer time scale w.r.t. the cell dynamics. Anarriving class-k VC is admitted iff

The admission region is

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Admission Regions

n1

n2

All allowable VCs

Service Separation with Dynamic Partitions

Equivalent Bandwidth

Peak Rate

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Admission Regions

n1

n2

n1

n2

Superimposed admission control boundary

Superimposed admission control boundary(Static Partitions)

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Strategy Parametrization If a functional form of the admission strategies has been fixed (e.g.,

Threshold or Complete Partitioning), in some instances it might be morepractical to determine the optimal parameter set by means of somemathematical programming procedure. In order to avoid integerprogramming, and to possibly use gradient methods, the problem can betransformed into an equivalent continuous parameter one.

A recent interesting procedure is the one introduced by Gokbayrak andCassandras, where at each descent (or ascent) step, the problem istransformed into an equivalent continuous one and back to discrete, byalways keeping the parameter values feasible (and thus applicable on-line).

Further simplification can be achieved by decomposing the problemhierarchically, and applying fixed “local” admission policies (based on a partof the state); the parameters characterizing the latter are chosen by acentral controller, playing the role of a coordinator in the hierarchicalscheme, by minimizing an overall cost function.

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A Hierarchical Control Example

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Routing

The issue of routing is a complex one, as it involves modelingthe whole network. There are different approaches in circuit-and packet-switched networks.

In multiservice networks, the problem is complicated by theneed to guarantee different QoS levels (QoS-aware routing).Multicast is another important aspect.

As regards routing at the “flow” or “connection” level of inelasticflows (as in circuit-switched networks), there is a vast literatureon adaptive and dynamic routing in this setting, which has beenextended to ATM and can be the basis for QoS routing andbandwidth allocation in an MPLS environment, among others.

Under fixed routing, the network at the connection level is aProduct Form Loss Networks. Blocking probabilities can becalculated efficiently by suitable approximations.

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Routing (cont’d)

Product Form Loss Networks

We consider approximations to compute blocking in a PFLN. Consider a network composed by J links, where link j has

capacity Cj bandwidth units (bu). There are K traffic classes,where class k has arrival rate λk, average connection duration 1/µk, bandwidth unit requirement bk, and a route Rk⊆{1,…,J}. Aclass k call is admitted only if bk bu’s are availble on each linkalong the (predefined) route. Blocked calls are lost. Arrivals arePoisson and independent, holding times may be general(invariant property) and are independent. Let ρk=λk/µk,K={1,…,K}, the set of classes that uselink j, and n=[n1,…,nK]. The state space is

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Routing (cont’d)

Product Form Loss Networks

The set of states where a class-k call is admitted is

As with the stochastic knapsack:

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Product Form Loss Networks (cont’d)

Product Bound

Suppose to have only single-service calls, i.e., bk=1,k∈K. Let

be the Erlang loss probability for a system with loadρ and C bu’s, and let

be the total offered load to link j, irrespective ofblocking on other links. The following bound holds:

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Reduced Load Approximation

From the Product Bound

Replace the ρk’s with ρktk(j), where tk(j) is the probability that atleast one bu is available in each link in Rk-{j}; the approximateprobability Lj that link j is full is given by

By assuming independence of blocking from link to link (whichis a further approximation),

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Erlang Fixed Point

Then, one has a Fixed Point Equation in L1,…,LJ of the form

The class-k blocking probability can then be approximated(again assuming independence) as

The fixed point equations can be written in compact form as

having defined

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Erlang Fixed Point

Under fixed routing, there exists a unique solution L*to the fixed point equation.

The solution can be found numerically in a number ofways, the most straightforward of which is repeatedsubstitutions

n being the stopping stage. Since, in general, T is nota contraction mapping, convergence is notguaranteed, though the iterates can be shown to getcloser and closer to L*.

The resulting approximate probability that a class-kcall is blocked does not exceed the product bound.

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Routing Flows (cont’d)

Dynamic Routing

The previous approximation was developed to computeblocking probabilities under fixed routing.

A task of network control is to decide dynamically on routing anincoming flow at “connection” (or Service Level Agreement) set-up.

There are a number of techniques developed for telephonenetworks and actually applied, starting during the 80’s, which gounder the name of dynamic routing.

They usually attempt to establish a connection on a direct (one-hop, either physical or virtual) route between a source-destination pair (or edge devices, in the multiservice Internetterminology), if any, and choose an alternative route thattraverses one or more switches (mostly one, i.e., a two-linkalternative), if the direct path is unavailable.

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Routing Flows (cont’d)

Dynamic Routing

There are a number of techniques to decide upon thealternative path, some of which can depend on the state (full orpartial) of the network at the time of decision.

In general, dynamic routing destroys the Product Form Solution,but useful approximations can still be derived to calculateblocking probabilities.

Trunk reservation is almost always used, in order to limitexcessive alternative routing during overload and because it hasdemonstrated a simple means to avoid network instabilities,reflected in convergence of the Erlang fixed point equation todifferent values.

Truly dynamic routing of data units, based on real-timedecentralized state information (in a team setting) is achallenging problem, which can be somehow efficientlyaddressed by means of neural parametric approximators.

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References

K.W. Ross, Multiservice Loss Models for Broadband TelecommunicationNetworks, Springer-Verlag, London, 1995.

H.J. Chao, X. Guo, Quality of Service Control in High-Speed Networks,Wiley, New York, NY, 2002.

J. Walrand, P. Varaiya, High-Performance Communication Networks,2nd Ed., Morgan-Kaufmann, San Francisco, CA, 2000.

D.P. Bertsekas, R. Gallager, Data Networks, 2nd Ed., Prentice Hall,Englewood Cliffs, NJ, 1992.

A. Girard, Routing and Dimensioning in Circuit-Switched Networks,Addison-Wesley, Reading, MA, 1990.

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