Adaptive Nonlinear Congestion Controller for a Differentiated-Services Framework

14 Pages·0.717 MB·English

by  Pitsillides A., Ioannou P., Lestas M., Rossides L.

94 IEEE/ACMTRANSACTIONSONNETWORKING,VOL.13,NO.1,FEBRUARY2005
Adaptive Nonlinear Congestion Controller for a
Differentiated-Services Framework
Andreas Pitsillides, Member, IEEE, Petros Ioannou, Fellow, IEEE, Marios Lestas, Student Member, IEEE, and
Loukas Rossides, Student Member, IEEE
Abstract—Thegrowingdemandofcomputerusagerequireseffi- queuesisanotoriouslydifficultproblem,evenforsimplecases
cientwaysofmanagingnetworktrafficinordertoavoidoratleast [1].Thisassertionisalsosupportedbythefactthatdespitethe
limitthelevelofcongestionincaseswhereincreasesinbandwidth
vastresearchefforts,spanningafewdecades,andlargenumber
arenotdesirableorpossible.Inthispaperwedevelopedandan-
ofdifferentcontrolschemesproposed,therearestillnouniver-
alyzedagenericIntegratedDynamicCongestionControl(IDCC)
scheme for controlling traffic using information on the status of sally acceptable congestion control solutions to address these
each queue in the network. The IDCC scheme is designed using challenges.
nonlinear control theory based on a nonlinear model of the net-
Itisworthnotingthatanumberofpopularcongestioncontrol
workthatisgeneratedusingfluidflowconsiderations.Themethod-
designs were developed using intuition, mostly resulting in
ology used is general and independent of technology, as for ex-
ampleTCP/IPorATM.Weassumeadifferentiated-servicesnet- simple nonlinear control schemes. One example is the eternal
workframeworkandformulateourcontrolstrategyinthesame congestion control solution deployed in the Internet Transport
spiritasIPDiffServforthreetypesofservices:PremiumService,
ControlProtocol(TCP)[2],[3]andsubsequent“fixes”[4]–[7].
OrdinaryService,andBestEffortService.Thethreedifferentiated
ItisworthnotingthattheAvailableBitRate(ABR)problem[8]
classesoftrafficoperateateachoutputportofarouter/switch.An
IDCC scheme is designed for each output port, and a simple to inAsynchronousTransferMode(ATM)haswitnessedasimilar
implement nonlinear controller, with proven performance, is de- approach, with popular congestion control schemes (see, e.g.,
signedandanalyzed.Usinganalysisperformanceboundsarede-
[9]–[11]) also developed using intuition, again resulting in
rivedforprovablecontrollednetworkbehavior,asdictatedbyref-
simplenonlinearcontroldesigns.Despitethead-hocapproach
erencevaluesofthedesiredoracceptablelengthoftheassociated
queues.Bytightlycontrollingeachoutputport,theoverallnetwork andtheirsimplicity,thesehaveshownremarkableperformance
performance is also expected to be tightly controlled. The IDCC andweredemonstratedtoberobustinavarietyofreallifeand
methodologyhasbeenappliedtoanATMnetwork.WeuseOPNET simulated scenarios. But, under certain conditions, empirical
simulationstodemonstratethattheproposedcontrolmethodology
andanalyticalevidencedemonstratethepoorperformanceand
achievesthedesiredbehaviorofthenetwork,andpossessesimpor-
tantattributes,ase.g.,stableandrobustbehavior,highutilization cyclic behavior of the controlled TCP/IP Internet ([12]–[14]).
withboundeddelayandloss,togetherwithgoodsteady-stateand This is exacerbated as the link speed increases to satisfy de-
transientbehavior. mand,andalsoasthedemandonthenetworkforbetterquality
IndexTerms—ATM, congestion control, differentiated-services of service increases. Note for WAN networks a multifractal
framework,Internet,nonlinearadaptivecontroltheory. behavior has been observed [15], and it is suggested that this
behavior—cascadeeffect—mayberelatedtoexistingnetwork
I. INTRODUCTION controls[16].
Tounderstand,andimportantlytopredict,thisdemonstrated
IT IS generally accepted that the problem of network con-
poor behavior is no easy task, especially since these schemes
gestion control remains a critical issue and a high priority,
are designed with significant nonlinearities (e.g., two-phase—
especially given the growing size, demand, and speed (band-
slow start and congestion avoidance—dynamic windows, bi-
width) of the increasingly integrated services demanded from
nary feedback, additive-increase multiplicative-decrease flow
fixedandmobilenetworks.Moreover,congestionmaybecome
control etc). The formal, rigorous, analysis of the closed loop
unmanageableunlesseffective,robust,andefficientmethodsfor
behaviorisdifficultifatallpossible,evenforsinglecontrolloop
congestioncontrolaredeveloped.Onecouldarguethatnetwork
networks. Furthermore, the interaction of additional nonlinear
congestion is a problem unlikely to disappear in the near fu-
feedback loops can produce unexpected and erratic behavior
ture; it is well-known that the optimal control of networks of
[17]. Clearly, proven effective congestion control schemes are
needed.
Manuscript received September 15, 2000; approved by IEEE/ACM Despitethesuccessfulapplicationofcontroltheorytoother
TRANSACTIONSON NETWORKING Editor L. Tassioulas. This work was sup-
complex systems (e.g., power, traffic, chemical plants, space
portedinpartbytheUniversityofCyprusandinpartbytheNationalScience
FoundationunderGrantNumberECS9877193. structures,aerospacesystems,etc.),thedevelopmentofnetwork
A. Pitsillides is with the Department of Computer Science, University of congestioncontrolbasedoncontroltheoreticconceptsisquite
Cyprus,CY-1678Nicosia,Cyprus(e-mail:[email protected]).
unexplored.Thisinspiteofthesignificantdemandsplacedon
P.IoannouandM.LestasarewiththeDepartmentofElectricalEngineering,
University of Southern California, Los Angeles, CA 90007 USA (e-mail: the network system overrecent years for the deliveryof guar-
[email protected];[email protected]). anteedperformanceintermsofqualityofservicetotheusers.
L. Rossides is with the Cyprus Telecommunications Authority, Nicosia,
Onemayattributethistothecomplexityofthecontrolproblem,
Cyprus(e-mail:[email protected]).
DigitalObjectIdentifier10.1109/TNET.2004.842238 coupled with the lack of collaboration between teletraffic en-
1063-6692/$20.00©2005IEEE
PITSILLIDESetal.:ADAPTIVENONLINEARCONGESTIONCONTROLLERFORADIFFERENTIATED-SERVICESFRAMEWORK 95
gineers and control systems theorists (though lately there are sendsfeedbacktothesourcestoregulatetheirrate.Severalap-
signs of increased collaboration). Most of the current conges- proachesforexplicitorimplicitfeedbacktothe sendercanbe
tion control methods are based on intuition and ad hoc con- adopted,aswellasconversionstoTCPtypewindow;theseare
trol techniques together with extensive simulations to demon- brieflydiscussedinSectionII-C.
stratetheirperformance.Theproblemwiththisapproachisthat TheIDCChasanumberofimportantcontrolattributes([25],
verylittleisknownwhythesemethodsworkandverylittleex- [22]),suchas:
planation can be given when they fail. Several attempts have
• It exhibits provable stable and robust behavior at each
beenmadetodevelopcongestioncontrollersusingoptimal[18],
port. By tightly controlling each output port, the overall
linear[17],[19]–[22],predictiveadaptive[23],[24],fuzzyand
network performance is also expected to be tightly
neural[25]–[27],andnonlinear[28]–[30]control.Despitethese
controlled.
efforts,thedesignofcongestionnetworkcontrollerswhoseper-
• It achieves high utilization with bounded delay and loss
formance can be analytically established and demonstrated in
performance.
practice is still a challenging unresolved problem. Recent ad-
vancesinnonlinearadaptivecontroltheory[31]offerpotential • It exhibits good steady-state and transient behavior; no
fordevelopingeffectivenetworkcongestioncontrollerswhose observable oscillations and fast rise and quick settling
propertiescanbeanalyticallyestablished. times.
Thispaperproposesagenericschemeforcongestioncontrol • Itusesminimalinformationtocontrolsystemandavoids
based on nonlinear and adaptive control ideas. It uses an inte- additional measurements and noisy estimates: (i) uses
grateddynamiccongestioncontrolapproach(IDCC).Aspecific onlyoneprimarymeasure,namelyqueuelength;(ii)does
problemformulationforhandlingmultipledifferentiatedclasses not require per connection state information; (iii) does
oftraffic,operatingateachoutputportofaswitchisillustrated. not require any state information about set of connec-
IDCC is derived from nonlinear adaptive control theory using tions bottlenecked elsewhere in the network (not even a
a simple fluid flow model. The fluid flow model is developed countoftheseconnections).Inordertoimprovespeedof
usingpacketflowconservationconsiderationsandbymatching response, an estimate of number of activesources at the
the queue behavior at equilibrium. While the fluid model may switch( )canbeuseful.However,insimulationsgood
notbethataccurateallthetimethecontroltechniqueusedtakes performancewasobtainedforaconstantvaluesettoone;
into account the presence of modeling errors and inaccuracies (iv) computes Ordinary Traffic allowable transmission
andminimizestheireffect. rate only once every ms (the control update period)
Recently, there is pressure on the Internet to transform into thereby reducing processing overhead. The controller is
amultiserviceshigh-speednetwork,see,e.g.,IntservandDiff- fairlyinsensitivetochoiceofvaluefor and .
Servarchitectures[32],[33].Lately,interestismainlyforDiff- • Itachievesmax/minfairnessinanaturalwaywithoutany
Serv architectures, as scalability problems have been reported additional computation or information about bottleneck
forIntserv.FollowingthesamespiritadoptedbytheIETFDiff- ratesofindividualconnections.
Serv working group for the Internet [33] we define classes of • It can guarantee a minimum agreeable service rate
aggregatedbehavior.Inthispaperwedefinethreeservices:Pre- withoutanyadditionalcomputation.
miumTrafficService,OrdinaryTrafficService,andBestEffort • Itworksoverawiderangeofnetworkconditions,suchas
TrafficService.Itshouldbenotedthatthemethodologyusedis roundtrip(feedback)delays(evaluatedfrom0to250ms
generalandindependentoftechnology,as,forexample,TCP/IP RTT), traffic patterns, and controller control intervals
orATM.TheproposedIDCCalgorithmcanbeclassifiedasNet- (evaluatedfrom32to353celltimes),withoutanychange
work-Assisted CongestionControl[34] anduses queuelength inthecontrolparameters.
informationforfeedback.Itisbecomingclear[35]thattheex- • Itworksinanintegratedwaywithdifferentservices(e.g.,
istingend-to-endTCPcongestionavoidancemechanisms,while Premium Traffic, Ordinary Traffic, Best Effort Traffic)
necessaryandpowerful,arenotsufficienttoprovidegoodser- withouttheneedforanyexplicitinformationabouttheir
vice in all circumstances. Basically, there is a limit as to how trafficbehavior.
much control can be accomplished from the edges of the net- • The proposed control methodology and its performance
work. Some mechanisms are needed in the routers to comple- areindependentofthesizeofthequeuereferencevalues
ment the endpoint congestion avoidance mechanisms, as sug- aslongastheyarebelowthesaturationpointoftheassoci-
gested by several researchers [36], [12], [37]–[39]. Note that atedqueues.Asaresultthenetworkoperatorcandynam-
the need for gateway control was realized early; e.g., see [2], ically steer the network operating region in accordance
whereforfutureworkthegatewaysideisadvocatedasneces- with global considerations, and has the flexibility to be
sary.ForTCPtraffic,thenewlydevelopedstrategies[36],[37], more or less aggressive, in accordance with the current
[35], [38], [39] advocate a more active router participation in networkanduserneeds.
thegenerationofamoreresponsivefeedbacksignal.Inpartic- • It has simple implementation and low computational
ular,RED[36]hasstimulatedaplethoraofactivities,including overhead.
extensiveevaluations and further techniques[40]. IDCC oper- • Itfeaturesaverysmallsetofdesignconstants,thatcanbe
ateslocallyforthePremiumTrafficService(notesimilarityin easilyset(tuned)fromsimpleunderstandingofthesystem
conceptwithRED[36])andfortheOrdinaryTrafficServiceit behavior.
96 IEEE/ACMTRANSACTIONSONNETWORKING,VOL.13,NO.1,FEBRUARY2005
This paper is organized as follows. Section II presents the
control problem and objective, and Section III illustrates the
formal derivation of the integrated dynamic congestion con-
troller(IDCC).Theanalyticperformanceevaluationofthede-
rivedalgorithmispresentedinAppendixesIandII.SectionIV
discussestheimplementationofIDCCandevaluatesitsperfor-
mance. The attributesdiscussedaboveare demonstrated using
simulations.Finally,SectionVpresentsourconclusions.
II. THECONTROLPROBLEMANDOBJECTIVE
Weproposeagenericschemeforhandlingmultipledifferen-
tiatedclassesoftraffic,usinganintegrateddynamiccongestion
controlapproach,derivedusingnonlinearcontroltheory.Bydif-
ferentiating each class, the control objective for each class is
“decoupled”fromtherest,thussimplifyingtheoverallcontrol
design.Thecontrolstrategyismodelbaseddynamicfeedback
linearization, with proportional plus integral action and adap- Fig.1. GenericoutputbufferedKinput-outputswitch.
tation.Itshouldbenotedthatthemethodologyusedisgeneral
andindependentoftechnology,asforexampleTCP/IPorATM.1
have relaxed delay requirements and allow their rate into the
Generically, we use the terms packet for both IP packets and
network to be controlled. These Services use any left overca-
ATMcells,andswitchforATMswitchandIProuters.
pacityfromthePremiumTraffic.Notethattoensurethatband-
widthisleftoverfromthePremiumTrafficServiceaminimum
A. ProposedDifferentiated-ServicesFramework
bandwidthmaybeassigned,e.g.,byusingbandwidthallocation
Recently, the DiffServ working group adopted two broad betweenservicesorconnectionadmission.Typicalapplications
aggregate behavior groups: the Expedited Forwarding (EF) includewebbrowsing,imageretrieval,e-mail,ftp,etc.
Per-Hop Behavior (PHB) [41] and the Assured Forwarding Finally, the Best Effort Traffic Service may belong to the
(AF) PHB [42]. The EF-PHB can be used to build a low loss, last class of the EF-PHB in a DiffServ architecture. It has no
low latency, low jitter, assured bandwidth end-to-end service, delayorlossexpectations.Itopportunisticallyusesanyinstanta-
thus indirectlyprovidingsome minimum“aggregated”quality neousleftovercapacityfrombothPremiumandOrdinaryTraffic
ofservice.TheAF-PHBgroupprovidesdeliveryofIPpackets Services.
in four independently forwarded AF classes. Within each AF
class,anIPpacketcanbeassignedthreedifferentlevelsofdrop B. Proposed Integrated Dynamic Congestion Control
probabilities.Eachclasscanbeprovidedwithsomeminimum Approach
bandwidth and buffer guarantees. We adopt the same spirit as Eachservicetransmitspacketstodestinationterminals.The
the IETF DiffServ working group [33] and divide traffic into packets from several Origin-Destination (OD) pairs traverse a
threebasictypesofservice:PremiumTrafficService,Ordinary numberofswitches onroutetothe destination.Each ODflow
TrafficService,andBestEffortTrafficService. maybeclassifiedasPremiumService,OrdinaryService,orBest
ThePremiumTrafficServicemaybelongtotheEF-PHBina EffortService.
DiffServarchitectureandisdesignedforapplicationswithstrin- We assume a generic output buffered switch as a reference
gentdelayandlossrequirementsthatcanspecifyupperbounds model.Theswitchhas inputand outputports(seeFig.1).
ontheirtrafficneedsandrequiredqualityofservice.Itisenvis- Each output port has a number of physical or logical queues:
agedthattheusermaycontractwiththenetwork.Theonlycom- oneforeachtrafficclass.Thereisapotentialbottleneckateach
mitmentrequiredbytheuserisnottoexceedthepeakrate.Note outputportoftheswitch,causedasaresultoftheratemismatch
thatpolicingunitsat theedgeofthe networkmayprovideen- betweentheflowintoandoutofthequeue.Sincethecauseof
forcementofthiscommitment.Thenetworkcontractthenguar- thebottleneckislimitedlinkcapacityattheoutputportsofthe
anteesthatthecontractedbandwidthwillbeavailablewhenthe switch, the congestion control scheme will be explained with
traffic is sent. Typical applications include video on demand, respecttoaspecificoutput-port(notethatthereisnocoupling
audio,videoconferencing,etc. between the output-ports). A congestion controller is installed
TheOrdinaryTrafficServicemaybelongtothefirstclassof ateachoutputport.Bytightlycontrollingeachoutputport,the
theAF-PHBinaDiffServarchitecture.Notethatdifferentprior- overallperformanceisalsoexpectedtobetightlycontrolled.
itiesmaybeassigned,withoutcomplicatinggreatlythedesign. At each output port of the switch we assume that dedicated
The Ordinary Traffic Service is intended for applications that bufferspaceisallocatedforeachoneofthethreeservicesand
thatthe servercanbesharedbetweenthethree inacontrolled
1Sincethispaperwassubmitted,IDCCwassuccessfullyintegratedwithin
RMD(ResourceManagementinDiffServ)framework,whichextendsDiffServ fashion(seeFig.2).PremiumServicerequiresstrictguarantees
principlestoprovidedynamicresourcemanagementandadmissioncontrolin ofdelivery,withingivendelayandlossbounds.Itdoesnotallow
IP-DiffServdomains.ThisworkwassupportedinpartbyECresearchproject
regulation of its rate (or at least regulation that will affect the
SEACORN:SimulationofEnhancedUMTSAccessandCoreNetworks,IST-
2001–34900,2002. given delay bounds). Any regulation of this type of traffic has
PITSILLIDESetal.:ADAPTIVENONLINEARCONGESTIONCONTROLLERFORADIFFERENTIATED-SERVICESFRAMEWORK 97
Section III. Once the common rate is calculated it is sent (fed
back) to all upstream sources. Based on the received common
rate, the source does not allow its transmission rate to exceed
this value over the next control interval. Note that any excess
sourcedemand(abovereceivedcommonrate)isqueuedatthe
sourcequeues,ratherthanbeallowedtoenterthenetwork,and
thuscausecongestion.
The Best Effort Traffic Service operates at the packet/cell
scale and uses any instantaneous left over capacity. This is
achieved by monitoring the combined server buffer at server
scheduler. In the absence of any packets in the server buffer
awaiting transmission it allows a packet from the Best Effort
Servicequeuetoentertheserverbuffer(bufferhasamaximum
oftwopackets;oneinserviceandoneinqueue).Notethatfor
Fig.2. Implementationofthecontrolstrategyateachswitch.
ATMthisfunctionmaybetrivial,butforvariablesizepackets
more care is required so that time sensitive packets are not
tobeachievedattheconnectionphase.Onceadmittedintothe
caughtbehindverylargeBestEffortpackets.
networkthenetworkhastoofferserviceinaccordancewiththe
givenguarantees.ThisisthetaskofthePremiumTrafficCon-
C. FeedbackSignallingSchemesforOrdinaryTraffic
troller. Ordinary Traffic on the other hand allows the network
As discussed above, for Ordinary Traffic the common rate
toregulateitsflow(paceit)intothenetwork.Itcannottolerate
(thefeedbacksignal)mustbecommunicatedtothesourcesfor
lossofpackets.Itcanhowevertoleratequeueingdelays.Thisis
action.Severalapproachesmaybeadopted.Indicatively,some
thetaskoftheOrdinaryTrafficController.BestEffortService
feedbacksignallingschemesinclude:usingfullfeedbackbyup-
ontheotherhandoffersnoguaranteesoneitherlossordelay.It
dating special fields in packets or cells (e.g., RM cells in an
makesuseofanyinstantaneousleftovercapacity.
ATMsetting[8],[10],[9]]orinTCPbymodifyingthereceiver
ForPremiumTrafficService,ourapproachistotightlycon-
window field in the TCP header [5] of a packet sent by re-
trolthelengthofthePremiumTrafficqueuetobealwaysclose
ceivertosource);usingExplicitCongestionNotification(ECN)
to a reference value, chosen by the network operator, so as to
indirectlyguaranteeacceptableboundsforthemaximumdelay asproposedfortheInternet[37],[38]andATM[8];usingim-
and loss. The capacityfor the Premium Traffic is dynamically plicit feedback, as for e.g., timeout due to lost packet [2], the
allocated,uptothephysicalserverlimit,oragivenmaximum. end-to-end approach in [34], using round-trip delay values as
Inthisway,thePremiumTrafficisalwaysgivenresources,upto indicatorsofthelevelofcongestion[7];aconversionfromrate
theallocatedmaximum( :maximumavailableorassigned towindowforTCPlikecontrol[43];orevenmoresophisticated
capacity,and :maximumbuffersize)toensuretheprovi- schemes,suchasadaptivebinarymarking[44],wheresources
sionofPremiumTrafficServicewithknownbounds.Duetothe change their rate according to variations in the binary signals
dynamicnatureoftheallocatedcapacity,wheneverthisservice presentinfeedbackstream,usingsimilarprinciplestoadaptive
has excess capacity beyond that required to maintain its QoS delta modulation (ADM) used in communication systems. In
at the prescribed levels (as set by the queue length reference thispaper,theimplementationdetailsofthefeedbacksignalling
value)itoffersittotheOrdinaryTrafficService.Thisalgorithm scheme are left for further study. For a simulative evaluation
usestheerrorbetweenthequeuelengthofthePremiumTraffic oftheproposedcontrolschemeweuseexplicitfeedback,pro-
queue andthereferencequeuelength asthefeedback videdbyupdatingspecialfieldsinpackets(RMcellsinanATM
informationandcalculatesthecapacity tobeallocatedto setting).
Premium Traffic once every control interval ms, based on
thecontrolalgorithmdiscussedinSectionIII. D. DynamicNetworkModels
TheOrdinaryTrafficServiceControllerregulatestheflowof Most of the current congestion control techniques use intu-
OrdinaryTrafficintothenetwork,bymonitoringthelengthof itionandadhoccontroltechniquestogetherwithextensivesim-
theOrdinaryTrafficqueueandtheavailablecapacity(leftover ulations to demonstrate their performance. The problem with
after the capacity allocated to Premium Traffic). The length this approach is that very little is known why these methods
of the Ordinary Traffic queue is compared with the reference workandverylittleexplanationcanbegivenwhentheyfail.The
value (could be chosen by network operator) and using a use of dynamic models could provide a better understanding
nonlinearcontrolstrategyitcalculatesandinformsthesources of how the network operates and can be used to develop con-
of the maximum allowed rate they can transmit over the next troltechniqueswhosepropertiescanbeestablishedanalytically
control interval. This algorithm takes into account leftover even when such techniques are based on intuition and ad hoc
capacity ,useserrorbetween guesses. For control design purposes the model does not need
queue length of Ordinary Traffic queue and reference tobeaccurate.Itisbecauseoftheinabilityofmodelingthereal
queue length , and calculates the common rate to worldaccuratelythatfeedbackwasinventedandcontroltheory
be allocated to the Ordinary Traffic users once every control iswidelyused.Agoodfeedbackcontroldesign(e.g.,basedon
interval ms, based on the control algorithm discussed in robust, possibly adaptive, control techniques [31]) should be
98 IEEE/ACMTRANSACTIONSONNETWORKING,VOL.13,NO.1,FEBRUARY2005
able to deal with considerable uncertainties and inaccuracies
thatarenotaccountedforinthemodel.
Usingtheaboveprinciple,belowwepresentaknownsimple
dynamic model, which we assume captures the essential dy-
namics, and is used for designing the proposed congestion
controller.
1) FluidFlowModel: Adynamicmodelissought,inaform
suitable for a distributed control solution. The objective is to
findamodelwhichcapturesthe“essential”dynamicbehavior,
but has low-order complexity, as, for example, relative to de-
tailed probabilisticmodels suchas the Chapman–Kolmogorov
equations for determining time-dependent state probability
distributionforaMarkovianqueue[45].Usingtheapproximate
fluidflowmodelingapproachproposedbyAgnew[46],various
dynamic models have been used by a number of researchers
[40], [45], [47]–[49] to model a wide range of queueing and
contentionsystems.Notethatseveralvariantsofthefluidflow Fig.3. TimeevolutionofnetworksystemqueuestateobtainedusingOPNET
model have been extensively used for network performance simulation(brokenline)andsolutionoffluidflowmodel(solidline).Theinput
tobothOPNETandfluidflowisthesameon–offsource(seeFig.5).
evaluation and control, see, for example, an early reference
that stimulated a lot of interest thereafter [50], and a recent
referenceofthepresentinterest[51]. Otherapproaches,suchassystemidentificationtechniquesand
Usingtheflowconservationprinciple,forasinglequeueand neuralnetworks,canalsobeusedtoidentifytheparametersof
assumingnolosses,therateofchangeoftheaveragenumberof thefluidflowequation.
cellsqueuedatthelinkbuffercanberelatedtotherateofcell We illustrate the derivation of the state equation for an
arrivalsanddeparturesbyadifferentialequationoftheform queue following [45]. We assume that the link has
a First-In–First-Out (FIFO) service discipline and a common
(1) (shared)buffer.Thefollowingstandardassumptionsaremade:
thepacketsarriveaccordingtoaPoissonprocess;packettrans-
where isthestateofthequeue,givenbytheensembleav- mission time is proportional to the packet length; and that the
erage of the number of cells in the system (i.e., queue + packetsareexponentiallydistributedwithmeanlength1.Then,
server)attime ,i.e., ; istheensemble fromthe queueingformulas,foraconstantarrivalrate
averageofcellflowoutofthequeueattime ;and isthe to the queue the average number in the system at steady state
ensembleaverageofcellflowintothequeueattime . is .Requiringthat when ,
Thefluidflowequationisquitegeneralandcanmodelawide thestatemodelbecomes
rangeofqueueingandcontentionsystemsasshownintheliter-
ature[45],[47]–[49].
(3)
Assumingthatthequeuestoragecapacityisunlimitedandthe
customersarriveatthequeuewithrate ,then isjust
The validity of this model has been studied by a number of
theofferedloadrate sincenopacketsaredropped.Theflow
researchers,including[47]and[48].
outofthesystem, ,canberelatedtotheensembleaverage
In[52]wepresentanexampleformodelinganOrigin-Des-
utilizationofthelink by ,where
tinationpathinapacketbasednetworkderivedusingfluidflow
isdefinedasthecapacityofqueueserver.Weassumethat
arguments and also demonstrate the ability of the fluid flow
canbeapproximatedbyafunction whichrepresentsthe
modelto model queueing systems by verifyingits behavior in
ensembleaverageutilizationofthequeueattime asafunction
comparison with an event based simulation using OPNET. A
ofthestatevariable.Thus,thedynamicsofthesinglequeuecan
typical time evolution of the queue state from both the model
berepresentedbyanonlineardifferentialequationoftheform
and OPNET simulation are presented in Fig. 3. We can ob-
(2) servethatthereisareasonableagreementbetweentheproposed
modelandtheobservedbehaviorofthesystem,assimulatedby
which is valid for and adiscreteeventsimulator,whichdemonstratesconfidencetothe
where is the maximum possible queue size modelforuseinthedesignofthecontrolsystem.
and themaximumpossibleserverrate. Note that similar fluid flow models in both the discrete
Different approaches can be used to determine . and continuous time form have been used by a number of
A simple, commonly used, approach to determine is researchersfordesigningoranalyzingthebehaviorofnetwork
to match the steady-state equilibrium point of (2) with that systems under control [14], [17], [19], [40], [53], [54]. For
of an equivalent queueing theory model, where the meaning example, Hollot et al. [40] using fluid flow arguments have
of “equivalent” depends on the queueing discipline assumed. developed a nonlinear dynamic model of TCP to analyze and
This method has been validated with simulation by a number design Active Queue Management (AQM) Control Systems
of researchers, for different queueing models [45], [47], [48]. using RED. For ATM, Rohrs [17] using similar fluid flow
PITSILLIDESetal.:ADAPTIVENONLINEARCONGESTIONCONTROLLERFORADIFFERENTIATED-SERVICESFRAMEWORK 99
arguments derived a discrete fluid flow model of the state Let , then where
of the buffer at the output port of an ATM switch, and used isthedesiredaveragestateofthePremiumTrafficbuffer.Then
this model to evaluate the performance of a binary Backward from (4)
Explicit Congestion Notification (BECN) control algorithm.
Hedemonstratestheundesiredcyclicbehaviorofthecontrolled
(6)
system. This (undesired) cyclic behavior is also presented in
[14] for TCP/IP, using dynamic models of the behavior of the
different phases of the TCP/IP congestion algorithms (slow where and is a constant indicating
startandcongestionavoidancephase)forhighbandwidth-delay themaximumratethatcouldbeallocatedtoincomingPremium
productsandrandomloss.Theirresultsaredemonstratedusing Traffic(e.g.,throughaconnectionadmissionpolicy)and
simulations. In [54] they use a similar model, as given by (3), isthephysicalcapacityoftheserver.
and intuition to design an ABR flow control strategy (referred Thecontrolobjectiveistochoosethecapacity tobeal-
to as queue control function) to keep the queue controlled. locatedtothePremiumTrafficundertheconstraintthatthein-
They use analysis and simulation to evaluate the proposed comingtrafficrate isunknownbutboundedby sothat
strategy. It is worth noting that many other types of models the averaged buffer size is as close to the desired value
have been proposed, either using queueing theory arguments, (chosenbytheoperatorordesigner)aspossible.Inmathe-
orothers,butinmostcasesthederivedmodelsaretoocomplex maticaltermsweneedtochoose sothat under
for deriving simple to understand and implement controllers. theconstraintsthat and .
Efforts to simplify these models for control design purposes Using feedback linearization and robust adaptive control
often lead to ignoring the dynamic aspects of the network ideaswechoosethecontrolinput,i.e.,capacity ,as
system. For example, in [55] the analysis of the performance
of simple (binary) reactive congestion control algorithms is (7)
carried out using a queueing theory approach model, which
is limited to steady-state analysis only due to the inability to (8)
handletheresultantcomputationalcomplexityforthedynamic
case. In this paper we explore the simple fluid flow dynamic where
model presented above (3) to demonstrate the derivation of
simpletoimplement,yetpowerfulcongestioncontroller. if
if (9)
III. PROPOSED INTEGRATED CONGESTION CONTROL if
STRATEGY:DESIGNANDANALYSIS
and
Ateachoutputportofaswitch,weimplementIDCC,theinte-
gratedcongestioncontrolstrategy(seeFig.2).IDCCisaninte- (10)
gratedstrategydevelopedforPremiumTraffic,OrdinaryTraffic
and Best Effort Traffic. It is based on the fluid flow model (3) where isaprojectionoperatordefinedas
usedtomodeltheinput-outputcharacteristicsoftheswitch(see
Fig.2),asfollows:
if
if
(11)
(4) if
otherwise
where is the measured (averaged) state of the Premium where ,and ,aredesignconstantsthataffectthe
Traffic buffer, is the capacity allocated to the Premium convergencerateandperformance.Thestabilityanalysisofthe
Traffic,and istherateoftheincomingPremiumTraffic. abovecontrolstrategyispresentedinAppendixI.
B. OrdinaryTrafficControlStrategy
(5)
Thecontrolstrategyisdevelopedusingthefluidflowmodel
(5)asfollows.
where is the measured (averaged) state of the Ordinary
Let , then where
Traffic buffer, is the capacity allocated to the Ordinary
isthedesiredaveragestateoftheOrdinaryTrafficbuffer.Then
Trafficand istherateoftheincomingOrdinaryTraffic.
from (5)
Model (4) is used to develop the Premium Traffic control
strategyandmodel(5)theOrdinaryTrafficstrategy.
(12)
A. PremiumTrafficControlStrategy
The selected control strategy for Premium Service is devel- Thecontrolobjectiveistochoose and sothatthe
opedusingthemodel(4)asfollows. averagebuffersize remainsclosetothedesiredvalue ,
100 IEEE/ACMTRANSACTIONSONNETWORKING,VOL.13,NO.1,FEBRUARY2005
chosenbytheoperatorordesigner.Thevalueof isgiven (18)
by (19)
(13) (20)
InotherwordsthecapacityallocatedtotheoutgoingOrdinary
where
TrafficiswhateverisleftafterallocationtothePremiumTraffic.
Using feedback linearization we choose the controlled traffic
(21)
inputrate as
(14) (22)
(15)
For computational reasons the computation of (11) is per-
formedindiscretetimeas
where is a design constant. The analysis of the above
controlstrategyisgiveninAppendixII.Notethattoachievede- (23)
couplingofthe stabilityand transientpropertiesofthe system
from time varying parameters, such as the number of connec-
tions ,thecalculatedcommonrate isdividedby , Then
anestimateof :
if
if (24)
(16)
otherwise
Theestimationalgorithmfor isaseparateresearchtopic. where ischosenas , is
Wehavederivedanalgorithm,basedonon-lineparameteriden- adesignconstant,and
tification techniques, which offers guaranteed convergence to
if
thetrue exponentiallyfast.Hereweareassumingthatsuch
if (25)
an estimate exists. This establishes that we can decouple the
otherwise
controlalgorithmfromthenumberofbottleneckedsessionsat
eachlinkandsotheanalysispresentedaboveisstillvalid.The if
simulation examples presented later show good performance, if (26)
evenwithusingaconstantvalueof whichexhibitsro- otherwise.
bustnessofthealgorithmwithrespecttoinaccuraciesinthees-
Remarks: is used at the switch output port by the
timationof .
scheduler to dynamically allocate capacity to the Premium
Traffic queue (see Fig. 2). The allocated capacity is held con-
C. BestEffortTrafficControlStrategy
stantovertheperiodofthecontrolinterval ms.
TheBestEfforttrafficcontrolleroperatesonaninstantaneous
Thecalculatedcommonrate issenttoeachoftheOr-
(packetorcell)timescale.Itutilizesanyinstantaneousleftover
dinary Traffic sources every ms using feedback signalling
capacity to transmit a packet from the Best Effort buffer. This
includedinRMcells,asdiscussedearlier.
increases the networkutilization during periods ofinsufficient
supplyofpacketsfromboththePremiumandOrdinaryTraffic B. Simulations
Services.
For the evaluation of the performance using simulation, we
useanetworkcomprisinganumberofATMswitches.Asdis-
IV. PERFORMANCEEVALUATION
cussedearlier,iftheATMswitchesarereplacedbyrouterssim-
Inthissectionweusesimulationstoevaluatetheperformance ilar performance is expected, if the calculated common rate is
ofIDCC.Wefirstpresenttheimplementationdetailsofthecon- signalledtothesourcesinasimilarfashion.
trolalgorithm,andthenthesimulationscenariosandsimulation 1) SimulationModel: OurATMnetworkmodelisshownin
results. Fig.4.ItconsistsofthreeATMswitches.Thisreferencemodel
has been designed to capture: the interference between traffic
A. ImplementationofIntegratedControlStrategy travellingadifferentnumberofhops;theinterferencefromreal-
Ateachswitchoutputport(seeFigs.1and2)weimplement time(Premium)trafficcompetingwithOrdinaryTrafficforthe
theintegratedcontrolstrategyderivedintheprevioussection. finite server resources; the effect of propagation delay on the
Thereferences , ,andthedesignconstants , , , effectivenessofthecontrolscheme;andthefairness(orlackof
and arefirstselected. it)amongtraffictravellingadifferentnumberofhops.
Ateachinstant ( )whichcorrespondstotime Using the reference model described earlier, we assume
,where isthesamplingperiod,wecalculate all queueing occurs at the output buffers of the switches and
that there is no internal blocking in the switch. In each ATM
(17) switchtherearethreeseparatelogicalbuffers(peroutputport)
PITSILLIDESetal.:ADAPTIVENONLINEARCONGESTIONCONTROLLERFORADIFFERENTIATED-SERVICESFRAMEWORK 101
Fig.4. Simulationnetworkmodel.
collecting Premium Traffic, Ordinary Traffic and Best Effort
Fig. 5. Ordinary Traffic source model. (a) Connection activity. (b) Packet
Traffic. The Premium Traffic buffers can accommodate 128
activity.(c)Cellactivity.Themodelparametersselectedforsimulationscan
cells, and the Ordinary Traffic buffer can accommodate 1024 beseeninTableI.
cells. Best Effort Traffic is selected to have infinite buffer
space.Thequeuesareservicedinaccordancewiththestrategy,
TABLE I
outlinedinSectionIII. ORDINARYTRAFFICSOURCEMODELPARAMETERS
WeusethesamenetworkmodelforthesimulationofATM
LAN and ATM WAN, but the distances between the switches
arechangedtoreflectthedifferentgeographicspansofthetwo
networktypes.IntheATMWANcase,thedelaybetweeneach
switch,duetothelinkdistanceissetat20msforeachlink,and
thedelaybetweenthelastswitchandthedestinationstationis
alsosetat20ms(thusaroundtripdelayof120msispresent).
to the destination without packet loss (after retransmission if
All of the links are assumed to transmit at 155 Mb/s. For the
necessary).
OrdinaryTrafficweconsider40connectionsattheedgeofthe
WehaveusedOPNETsimulationtoolsforourexperiments.
network (20 are connected directly to ATM switch 0, and 10
UsingsimpleunderstandingoftheATM,wesetthe controller
ineachofATMswitches1and2),whichcanhavetheirtrans-
designconstantsasfollows.
mission rate controlled by the network. Three of the Ordinary
ForthePremiumTrafficcontroller:
Trafficflowpathsare1-hoppaths,andoneisa3-hoppath.Also
for a physical buffer size of 128 cells,
fourVBRandtwoCBRsourcesaredirectlyconnectedtoATM
, , , .
switch 2 (1-hop path) representing Premium Traffic. Each Or-
FortheOrdinaryTrafficcontroller:
dinary Traffic terminal generates traffic based on a three-state
for a physical buffer of 1024
model (see Fig. 5 for model, and Table I for the selected pa-
cells, , .
rameters).Inthe idlestatenotrafficis generated.Theidlepe-
The control update period ms was set at several values
riodisgeneratedfromageometricdistributionwithameanpe-
( celltimes ms, 75 celltimes, 175 celltimes, and
riodchosentoadjusttheofferedloadonthelink.Intheactive
celltimes ms)inordertoinvestigatethesensitivityof
state the source generates a series of packets or bursts which
controltothevalueofthecontrolupdateperiod.
are interspersed by short pauses. The period of each pause is
drawnfromanegativeexponentialdistribution.Thepacketsize
C. SimulationResults
and the number of packets generated during an active period
arealsogeometricallydistributed.WehaveconsideredtheOr- 1) SteadyStateandTransientBehavior: Usingthesimula-
dinary Traffic source terminal buffers as infinite. Each VBR tionmodelweevaluatetheperformanceofATMLANandATM
sourceissimulatedbyusingtheautoregressivemodelproposed WAN.
byMaglarisetal.[56](weconsideravideosourcewith480000 As noted previously, Premium Traffic (CBR/VBR sources)
pixels/frame).TheCBRsourcegenerates25Mb/sandpacesthe hasapriority.Wecanguaranteethemmaximumqueueingde-
cells into the network uniformly. In case of cell losses, which laysnotexceedinginanaveragesensethesumofthereference
occurduringtheperiodsofcongestion,weuseasimpleretrans- valueofeachofthebuffersinthepath,assetbythenetworkad-
missionprotocol.Apacketispresumedtobelostevenifasingle ministrator.Inordertotesttheresponsivenessofourcontroller
cellislost.Packetsthatarereceivedbythereceiveterminalwith (transientbehavior)wesetavariablereferencepointforthisser-
missingcellsareretransmittedbythesourceuntilsuccessfulde- vice. At the beginning we set the reference point to 100 cells.
livery. The ”useful network throughput” represents the actual After sitissetto50cellsandafter sitisagain
throughput of packets (in Mb/s) that are eventually delivered raisedto100cells(where standsfortimeinseconds).Inthis
102 IEEE/ACMTRANSACTIONSONNETWORKING,VOL.13,NO.1,FEBRUARY2005
Fig. 6. Switch 2 (last switch) time evolution of Premium Traffic queue
lengthforaLANandWANfor140%loaddemand.Notethatasthefeedback
information is local, there is no deterioration in performance due to the
increasedWANpropagationdelay.
waywenotonlyshowthatourcontrollercanmatchtherefer-
encevaluesbutthatitcanalsocopewithdynamicchangesthat
occur in the network (e.g., another connection is set up, more
bandwidthisrequiredforreal-timeservices,etc).Tosimulatea
morerealisticscenario,wealsochangethereferenceontheOr-
dinaryTraffic.Sincewecanaccepthigherdelaysthereference
valuesaresetat900cellsfor s.Afterthattimeitissetto
300cellsuntil sandafter sitisraisedto600cells.It
canbenoticedthatthereferencepointchangesbetweenthePre-
miumandOrdinaryTrafficarenotsynchronizedbetweenthem.
Note that the Premium and Ordinary Traffic sources generate
traffic according to a realistic scenario (they are not saturated
sources).Thecontrolledsystemperformanceforthecaseofan Fig.7. Switch2(lastswitch)timeevolutionoftheOrdinaryTrafficqueue
length.(a)LANand(b)WANfor140%loaddemand.(Thecontrolperiodvaries
ATMunder heavy load (140%) is demonstrated here, for both
between32celltimes(cid:17)0:085msto353celltimes(cid:17)0:94ms).
aLANandaWAN.Fig.6showsthebehaviorofthePremium
Traffic.Asexpectedthecontrolledsystembehavioristhesame
forbothWANandLANnetworks,asthefeedbackislocal.In roundtriptimeofabout120ms.Also,theobserveddeteriora-
Fig.7thebehavioroftheOrdinaryTrafficqueuelengthisshown tionduetothetenfoldincreaseincontrolperiodisacceptable.
with varying control periods for both LAN and WAN config- Observethatforthe caseofPremiumTrafficqueue(Fig.6)
urations. The most heavily congested switch (Switch 2) is se- thereferencepointmatchesexactlytheobservedbehavior(100
lected,whereOrdinaryTrafficcompeteswithPremiumTraffic cells and 50 cells). However, in the case of Ordinary Traffic
forthescarcenetworkresources.Thefigureshowsthatthecon- (Fig.7)asizeableoffsetisobservedforeachreferencesetting.
troller adapts very quickly to reference point changes (could Notethatintroducingintegratingactioninthecontrollercanrec-
be likened to abrupt changing network conditions), as well as tifythisoffset,howeveronecanarguewhethertheextracom-
showing a reasonable insensitivity to control periods ranging plexityisjustified,asanexactreferencevaluemaynotbenec-
from 0.085 ms to 1 ms (a more than 10 tenfold increase). It essaryforthisservice.
is very important to notice that there are no observable over- We have also monitored the queue length behavior for
shoots and undershoots (except for the undershoot at 0.5 s for Switch 0 and Switch 1. We observe that both queues are well
thelongestcontrollerperiodof1ms),nooscillationsorcyclic controlled with no overshoots or undershoots exceeding 2%.
behavior,andthatthecontrolledsystemrespondsveryquickly Forbothswitches,thereferencepointissetequaltoaconstant
to the changes introduced in both queues. In other words, the 600 cells for the Ordinary Traffic and the Premium Traffic is
system exhibits a good transient behavior. So we can say that settozero.Notethateventhoughthe3-hoptrafficbehavioris
we can dynamically control the buffer state and the sources dictatedbythebottleneckswitchdownstream(Switch2)there
sendingrate,whichinturnimpliesthatthenetworkiswellcon- is no observable performance degradation. Again, an offset
trolled and congestion is avoided, or quickly controlled. Note fromthereferencevalueisobserved,whichcanberectifiedby
thatthecaseoftheWANexhibitscomparableperformancewith introducingintegratingaction.
theLAN,eventhoughthepropagationdelay(andthereforethe The throughput for the bottlenecked switch was also moni-
forwardandfeedbackdelay)havesubstantiallyincreaseddueto tored,exhibitingaconstantandcloseto100%utilization; 98%
PITSILLIDESetal.:ADAPTIVENONLINEARCONGESTIONCONTROLLERFORADIFFERENTIATED-SERVICESFRAMEWORK 103
Fig. 9. Typical behavior of the time evolution of the transmission rate
of controlled sources using Switch 2. (a) LAN configuration. (b) WAN
configuration.
Fig.10. Networktestconfigurationfordemonstratingdynamicbehaviorand
fairness.
the leftover capacity. All Ordinary Traffic sources should dy-
namicallysharetheavailablebandwidthwithnodiscrimination,
for example due to their geographic proximity to the switch.
Everysourcesendswiththesamerules.Thefairnessshownby
IDCCcanbeinferredfromFig.9foranumberoftypicalon–off
Fig. 8. Typical behavior of the time evolution of the common calculated sources.Toclearlyillustratethefairnessofourschemeweadopt
allowedcellrateatswitch2.(a)LAN.(b)WAN.
nextasimilarapproachtootherpublishedworks.
WeselectthenetworktestconfigurationshowninFig.10and
fortypicalsimulationruns.Thisisveryimportantsincethecon- setallsourcestobesaturated(i.e.,alwayshavecellstotransmit).
trollernotonlyavoidscongestionbutalsofullyutilizestheavail- The chosen configuration allows easy interpretation of the ex-
able resources, even for demands considerably exceeding the pectedbehavior.Itisselectedtodemonstratethefairnessinthe
availablelinkcapacity(140%inthiscase). presenceoflargedisparityindistancefromtheswitches(local
The time evolution of the calculated common allowed cell andfarsources)andaggressivenessandadaptabilitytodynamic
rate forthe congestedswitch isshowninFig.8forbothLAN changesinthenetworkstate.
and WAN, for 140% load demand. Note that this common al- InFigs.11and12wedemonstrate aggressiveness,fairness,
lowedcellrateissenttoallsourcesusingthisswitch.Thisrate andadaptabilityofthecontrolschemeforbothLANandWAN
isusedbythesourcesasthemaximumratethattheyareallowed network topologies. We let the 3-hop traffic start transmitting
totransmitoverthenextcontrolupdateperiod.Thetimeevolu- at , thus all link bandwidth is totally available to the
tionofthetransmissionrateofanumberofcontrolledsources 3-hop traffic. The 1-hop-a traffic at switch 0 is next started
isshowninFig.9.Inthefigure,3-hopand1-hop-csourcesare at , thus forcing the 3-hop traffic to share equally the
shownforbothLANandWANnetworks.Notethatthesources availablebandwidthbetweenthem.At thetwo1-hop-b
arenotsaturated.Thesourceratesquicklyadaptfairlytotheir sourcesarestartedatswitch1,thusforcingthe3-hoptrafficto
steady-statevalues,eventhoughthe3-hopsources,inthecase share the available link bandwidth between the three sources
of the WAN, are located about 12000 km away (equivalently competing for it at switch 1. Their fair share is 51.6 Mb/s
60msdelayforcellsbeforetheyarriveattheswitch).Theissue ( 117000cells/s).Sincethe3-hoptrafficwasforcedtoreduce
offairnessisdiscussednext. its rate by switch 1, it now leaves some unused capacity at
2) Fairness: Fairness is another important attribute of any switch 0, which the 1-hop-a source quickly takes up, i.e., at
congestion control system. Of course, fairness in networks is the 1-hop-a source increases its rate from 77.5 Mb/s
relative.SincewehavePremiumTrafficServicesandOrdinary ( 175000cells s)to90Mb/s( 204000cells s),takingup
Traffic Services it means that the latter must be satisfied with theextracapacity.Similarly,at whenthethree1-hop-c