QoS-aware routing schemes based on hierarchical load-balancing for integrated services pack

Abstract—This paper presents a load balancing method to improve network utilization when static routing algorithms are employed. Static routing algorithms can generally be reduced to a path assignment problem with the aim of minimizing a cost function: i.

QoS-AwareRoutingSchemesBasedonHierarchicalLoad-BalancingforIntegratedServicesPacketNetworks

C.Casetti,R.LoCigno,M.Mellia

DipartimentodiElettronica,PolitecnicodiTorino,Italy

E-Mail:casetti,locigno,mellia@polito.it

Abstract—Thispaperpresentsaloadbalancingmethodtoimprovenet-workutilizationwhenstaticroutingalgorithmsareemployed.Staticrout-ingalgorithmscangenerallybereducedtoapathassignmentproblemwiththeaimofminimizingacostfunction:i.e.,maximizingnetworkrevenues.Unfortunatelytheproblem,whenmultipleconstraintssuchasdifferentQoStraf cclassesarepresent,iscomputationallyintractable.Loadbal-ancingmethodsareheuristicsthatallowtheidenti cationoflocalminimaofthecostfunctionthathopefullyareclosetotherealoptimum.

Theloadbalancingmethodweproposeisbasedonlyonstaticinfor-mationabouttheaveragetraf cloadofeachtraf crelation:apieceofinformationwhichcaneasilybeattainedintelecommunicationnet-works.Thepath-selectionstrategyisde nedintermsofSetTheoryanditsperformanceisevaluatedviasimulationbycomparisonagainststandardMinimum-Hoppathselections.Simulationresultsshowthatlowprioritytraf cbene tssigni cantlyfromthemorebalancedloadobtainedwithoursolution.

I.INTRODUCTION

Integrated-ServicesPacketNetworks(ISPN)areemergingasoneofthenewchallengesinnetworkingresearch.ISPNisnotyetacompletelyde nedterm:theassumptioninthisworkisthatwedealwithapacket-switchednetworksupportingtwoormoretraf cclassesdifferentiatedbytheirrequiredQualityofService(QoS).NextgenerationInternetwillbe(hopefully)anISPN,butAsynchronousTransferMode(ATM)networksareISPNsaswell,withtheadditionalconstraintofhandlingonly xed-sizepacketsnamedcells.

RoutingstrategiesplayanimportantroleinISPNs,sinceitisexpectedthattheyhavewide-areacoverageandtheyarehighlymeshed.QoS-awareroutingtakesintoaccountalsothecharac-teristicsoftheconnectionthatisbeingroutedthroughthenet-work,inordertoexploitnetworkresourcestotheirfullextent.Traditionally,routingstrategieshavebeendividedintostaticanddynamicones.Dynamicroutingstrategies[1],[2],[3]areveryappealingfortheircapacitytodealwithunpredictablechangesintraf cpattern;however,inverylargenetworks,theysufferfromthestaleinformationproblem:routingdecisionsaretakenonestimatesofthenetworkconditionthatmaybeeitherwrongorout-of-dateandthismayinduceinef cientnetworkexploitationand,ultimately,evennetworkoscillationandcol-lapse[4].Staticroutingstrategiesaregenerallynotbasedonthenetworkload,butontopologicalpropertiesofthenetwork,suchasthenumberofcrossednodes,thelengthandthecapacityofthelinks,andsoforth.Agoodexampleofdifferentstaticrout-ThisworkwassupportedinpartbyaresearchcontractbetweenCSELTandPolitecnicodiTorinoandinpartbytheItalianGovernmentthroughtheMin-istryforUniversityandResearch(MURST)andthroughtheNationalResearchCouncil(CNR).

ingstrategiescanbefoundin[5].Inourworkwefocusonstaticroutingstrategies,leavingforfutureresearchacomparisonwithdynamicones.

Theperformanceofstaticroutingalgorithmscanbeenhancedmakinguseofsomestatisticalknowledgeofthetraf c,suchasthelong-termaverageofthetraf cofferedtothenetworkfromnodetonode.Inanycase,theaimofanystaticrout-ingalgorithmistheidenti cationofthesetofroutes,forany

,thatoptimize(oratleastenhance)sourcedestinationpair

thenetworkperformance.Theidenti cationoftheoptimalsetofroutesisgenerallyaNP-Completeproblemwhenmultipleconstraintsarepresent[6],[7],henceapproximationsorheuris-ticsareneededtoobtainroutingalgorithmswithgoodperfor-manceinISPNnetworks,especiallyifmultipleserviceclassesarepresent.

Ourworkintroducesaload-balancingheuristicsthatcanbehierarchicallyappliedtodifferenttraf cclassesforthede ni-tionoftheroutesetstobeusedbyalternate-path(primary-pathonlycanbeseenasaspecialcase)routingschemes.AlternateroutesaresequentiallyprobedastheCAC(ConnectionAdmis-sionControl)functiondeniesallocationonthechosenpath.WepointoutthatroutingandCACfunctionsarenottightlycoupled,sothat,forinstance,astaticroutingalgorithmcanbecoupledwitheitherastaticCAC(e.g.,peakorequivalentbandwidth)orwithadynamicCACbasedontraf cmeasures.

Theremainingpartofthepaperisorganizedasfollows:Sec-tionIIgivesaformalde nitionoftheproblem,inordertoallowageneralandtheoreticalanalysis;SectionIIIdescribesthepathsselectionalgorithmsusingtheformalismde nedinSectionII;SectionIVdescribesthescenariochosenforresultscomparison,andSectionVpresentsthenumericalresultsobtainedbysimu-latingtheabovescenario;SectionVI, nally,closesthepaperwithhintsontheprosecutionofthework.

II.SETTHEORYPROBLEMFORMULATION

ALGORITHMDESCRIPTION

AND

Letusconsideranetwork,whereisthesetof

and.nodesandisthesetoflinks,andlet

1

thesetofallpossibleloop-freepaths,andWedenoteby

thesetofallpossible1loop-freepathsbetweentheby

sourcenodeandthedestinationnode.Obviously

.Letbeagenericpath,andbethei-th

bethesetofallpathfromsourcetodestination.Letalso

thesetofallpossiblepossiblepathssharingthelink,and

Abstract—This paper presents a load balancing method to improve network utilization when static routing algorithms are employed. Static routing algorithms can generally be reduced to a path assignment problem with the aim of minimizing a cost function: i.

2

pathsfromtosharingthelink.Letbeagenericcostfunctionassociatedtothepath,

canbearelatedtothenetworktopology;forexample,

functionofthephysicallengthof,orofthenumberofhops

,orafunctionofboth.Giventwopaths

connectingthesamesourceanddestination,theyareconsid-.Weshallalsodenotebyered-equivalentif

thenumberof-equivalentpathsofcostfromto

.

,whereastaticroutingalgorithmisGivenanetwork

employed,letusconsidertheproblemofhowtoorderthesetofallpossiblepathstobetterexploitthenetworkcapacity.

,thesortingalgorithmhastochooseWhenever

betweentwoormoreequivalentpaths:asupplementarymetrichastobede ned.Tothispurpose,letusde nesomenewparam-,whereeters.Supposethatweknowthetraf cmatrix

istheprobabilitythatasourcetriestoopenacalltoward

betheofferedloadofsource.Weshalladestination.Let

anothercostfunction,derivedfromtheband-denoteby

widthrequirementoftheconnectionoriginatedatthesourceandroutedtothedestination;wethenhave.Thisiscalled“StaticOfferedLoad”,representingtheloadthataconnectionofferstothenetwork,evaluateduponthestaticpa-rametersofthetraf cmatrix.

Withtheabovenotation,wecancomputea“StaticLinkCost”

foreachlinkofthenetwork,de nedasfollows:function

Forthesakeofsimplicity,we rstde neasetofsimplepro-ceduresthatarelateronusedtoobtainthealgorithmweare

interestedin.

).ProcedureHopFirst:HF(

containingallthepathsGivenasetofpaths, ndasubset.withtopologicalcost

1.foralldo

then2.if

3.

4.return;

).ProcedureMinHop:MH(

foreachGivenasetofpaths, ndtheminimumcost

source-destinationpair,andreturnthesubsetcontainingalltheminimumcostpaths.

,fordo1.for

;2.

3.

4.return

HF

;

whereistheavailablebandwidthonthelink.Wedeliber-atelydidnotspecifyfurtherthenatureof,sincethisquantitycanbeusedtokeepintoaccounthigher-prioritytraf cthateffec-tivelyshrinksthelink’scapacityasfarasthethelower-prioritytraf cisconcerned(thisisthecaseofbest-effortvs.guaran-representsthenormalizedloadthatthelinkteedtraf c).

wouldcarryifwetookintoaccountthetraf cresultingfromallsource-destinationpairsthatroutecallsoverthesetofpaths.Again,theterm“static”meansthatthiscostisevaluatedontheknowledgeofthetraf cmatrixonly,anditisnotarealmeasureofthecarriedload.However,itshouldbepointedoutthat

isupdatedthroughttheroutecomputationphaseasthestatic-canloadalgorithmkeepsaddingnewpaths.Notealsothat

begreaterthanone.

Bymaximizingoveralllinksofapath,wecanderivea

forthatpath:“StaticCost”

).ProcedureEquivalentPath:EP(

containingallthepathsGivenasetofpaths, ndasubset

withanumberof-equivalentpathsequalto.

,fordo1.for

2.3.ifthen

;4.

5.return

Thefollowingproceduresrelyonvector,whichisthe

isinitializedtozeroaccumulatorfortheStaticLinkCost.

andisupdatedwhenevertheSCUprocedure(seebelow)isexe-cuted.

ProcedureStaticCostUpdate:SCU().

foritslinks.Givenapath,updatetheStaticLinkCost

1.letandbethesourceanddestinationnodeslinkedby;

do2.foralllink

3.

Wecanthuschoosebetweentwo(ormore)-equivalentpaths

,sortingthemaccordingtothecost.

ProcedureStaticLoadSorting:SLS().

Givenanunorderedpathset, ndanorderedsubsetofpaths

.NotethatwiththeminimumStaticCostforeachpair

thisistheonlyprocedurethatprovidesanorderingoftheinputsetofpaths.1.2.fordo

;3.

2

suchthat4. nd

5.;6.SCU();7.

8.return;

III.ALGORITHM

DESCRIPTION

A.HierarchicalLoadBalancingAlgorithm

Whenmultipletraf cclassesarepresent,withdifferentQoSrequirementsaswellasdifferentpriorities,thepathassignment

Ifthereismorethanoneminimumcostpath,onecanrecursivelychoosebetweenthemagainrecalculatingonallthelinksexceptfortheoneforwhich.Atlast,onecanchoosebetweenthemrandomly.

Becausethetargetoftheloadbalancingalgorithmsistoor-derasetofpath,wechosetodescribethesealgorithmsinaset

theorymanner,whereorderingfunctionscanbeapplied.

orasubsetofthem,aslimitedbytherouteselectionalgorithm

Abstract—This paper presents a load balancing method to improve network utilization when static routing algorithms are employed. Static routing algorithms can generally be reduced to a path assignment problem with the aim of minimizing a cost function: i.

3

proceduremustbeawarethatconnectionswillbeacceptedbyCACfunctionsfollowingdifferentcriteria.CACfunctionsandpacketschedulers,generallyassumehardclassseparationwithacceptancepreemption,i.e.,regardlessofthenetworkbeingal-readysaturatedbylowprioritycalls,ahigherpriorityonewillbeaccepted,anditspacketswillbeservedwithpriority,thatisinnonFIFOorder,oncetheyareinthenetwork.AsfasasCACandschedulingareconcerned,ahierarchicalpathselectiontech-niquebasedonloadbalancingshouldbeanappropriatesolutiontohelplow-prioritytraf ctoavoidroutesheavilyusedbyhigherprioritytraf c.

bethesetofavailablepathsinthenet-Let

work.BydividingitintodifferentsubsetsandorderingthemaccordingtotheStaticCostfunction,weobtainapathas-signmentfromthesourcestothedestinations,achieving,hopefully,abetterexploitationofthenetworkcapacitythanbysimpleMinimum-Hopordering.NoticethatMinimum-Hopor-deringyieldsexactlythesamepathselection,regardlessofitbeingrunonalltraf cclassestogetherorhierarchicallyclassbyclass.

Wedescribeasinglesortingcriteria,althoughmoreheuristicswerestudiedin[8],andobviouslymanymorecanbede ned.Thealgorithmworksincycles:ineverycycle,itassignoneandonlyonepathpersource-destinationpair,ifitexists,startingfromthepathswiththeminimumnumberofhops.

Forthesakeofclaritythealgorithmisdescribedforasin-gletraf cclass,avoidinganadditionalloopontraf cclassesandtheconsequentcomplicationinthenotation.Hierarchically

isre-movingfromoneclasstothenext,thestaticlinkcost

ofhigher-QoS-classessourceswhosesettothestaticload

belongsto.Wechosenottotakeintoac-primarypath

counttheloadduetosecondarypathsfromhigherclasses,sincesecondarypathsarelesslikelytocarrynewlyactivatedcallsthanprimarypaths.

5.;

=EP();6.

;7.

;8.

do9.for

;10.

do11.while

=HF12.

=SLS(13.

14.

15.return;

;

);

;

Fig.1.AlgorithmBalancedPrimaryFirst(BPF)

IV.SIMULATIONSETUP

Theeffectivenessofthealgorithmpresentedintheprevioussectionswasstudiedbymeansofacall-levelsimulationtoolforhigh-speednetworks,calledANCLES[9][10][11],assumingtwotraf cclasses:ahighpriority,guaranteed-QoSclassandalowpriority,best-effortclass.ThenetworktopologyofchoiceisshowninFig.2;itcombinesarathertightmeshwithhundredsofloop-freepathsandalocalizedbottleneck.Thelinkspeed,whichisthesameforalllinks,isequalto500Mb/s.Amixofconstant-andvariable-bitratesources,locatedineverynode,areassumedtogeneratetraf cinthehighestQoSclass:the

Mb/srateconstant-bitratesourcestrytoopencallsat

towardeachother,(callholdingtimesaredeterminedbyi.i.d.exponentialrandomvariablesaveragingat500seconds);the

Mb/swhich,variable-bitratesourcesactivatecallsat

onceactivatedandadmittedtothenetwork,holdforanexponen-tiallydistributedperiod,withaverage1000seconds;variable-bitratecallsexhibitaburstinessdegree(peak-to-meanrateratio)

Mb/s.equalto5,thusresultinginanaveragerate

Thecalladmissioncontrolschemetowhichtheabovecallsaresubjectisrathersimple;foreachlink,newcallsareacceptedif:

(1)

B.Algorithm:BalancedPrimaryFirstBPF()

Thefollowingalgorithmassignsateveryloopasinglepath

(ifitexists)fromthesourcetothedestination,resort-ingtheremainingpathset,inorderto ndthebestpathtoas-signinthenextcycle.Thisisobtainedbyapplying,insequence,theMinHopalgorithmtosetasidealltheshortestpathsforallsource-destinationpairs,thentheEquivalentPathalgorithmtoidentifyallthesubsetswith-equivalentpaths.EachsubsetisprocessedbytheHopFirstalgorithmwhich,inturn,yieldsasub-subsetofshortestpaths.Eventually,theStaticLoadSort-ingalgorithmisusedoverallsub-subsetsidenti edabovetoobtainthe nalorder,asshowninFig.1.Theresultisare-,thereorderedpathssetwhere,foreachtraf crelation

inwhichthe rstoneistermedisanorderedpathssub-set

primaryandalltheothersaretermedsecondary.Theroutingfunctionprobesallthepathsinorderandtheconnectionisre-fusedonlyiftheCACfunctionscannotallocateitonanypaths

,asisdoneintheUncontrolledAlternateofthesub-set

Routing[5].

do1.while

=MH();2.

;3.

do4.while

andarethesetsofconstant-andvariable-bitratewhere

calls,respectively,isthelinkcapacity,andisaprotection

)thatcanbesetsoastoavoidthatthewholecoef cient(

Abstract—This paper presents a load balancing method to improve network utilization when static routing algorithms are employed. Static routing algorithms can generally be reduced to a path assignment problem with the aim of minimizing a cost function: i.

4

1e+00

1e-011e-02

no lbwith lbγ = 0.4γ = 1

1e-03

1e-04

1e-05

1.5

1.61.7

Load

1.81.92

3.Callblockingprobabilitiesasafunctionoftheoverallguaranteed-class

networkloadinGb/s

andingconnectionswithacellratevaluemidwaybetween,accordingtoafactor;thatis:

(2)

AdiscussionoftheCACschemejustdescribedanditsrelationtosomeequivalentbandwidthexpressionscanbefoundin[12].

and(and,forInoursimulations,wechose

,yieldingpeakallocation).someresults,

Forwhatconcernsbest-effort,lower-priorityusers,nodesN1,N8andN12arerequestedtoactivateconnectionswith

(butwealsoreportresultswithapeakrate

)andaverageholdingtimeequalto60seconds.

Eachbest-effortsourceequallydirectsitstraf ctowardnodesN4,N6andN10.Theactualbandwidth,possiblysmallerthanthepeak,exploitedbyusersofthisclassisdeterminedbyamax-minfairnessallocationschemethat,foreachcall,accountsforthenumberofcallsonthebottlenecklinkandfortheresidualcapacityavailabletothebest-effortclass1.NoCACisimple-mentedforbest-effortcalls.

Thenetworktraf cwassplitamongguaranteed(40%oftheoveralltraf c)andbest-effort(60%)calls.Also,callsareroutedaccordingtotheHierarchicalLoadBalancingAlgorithmde-tailedinSubsectionIII-A;notethat,sincethereisnoCACforbest-efforttraf c,allcallsinthisclassareroutedovertheirre-spectiveprimarypaths.

Soastoprovideaninsightintothecomplexityoftheloadbal-ancingalgorithmsweareproposing,weestimatedthatsortingallpossiblepathsofthenetworkinFigure2(approx.40,000paths)requiredjust2secondsonaPentiumII-266MHzwork-station.

ingandCACalgorithmsweredeployed,withoutpreventivelybalancingtheload(i.e.sortingthesetoftheavailablepathsonlybytopologicalcost).Figure3showsthecallblockingprob-abilitiesforguaranteedtraf cwhichwereestimatedasafunc-tionoftheoverallguaranteed-classloadofferedtothenetwork(inGb/s),whendifferentvaluesof,rangingfromapeak-rate

)toamorecharacterizationofvariable-bitratesources(

).Solidlinesrefertocurvesobtainedwith-relaxedone(

outloadbalancing,whiledashedlinesrefertotheloadbalancingalgorithm.

Itcanbeobservedthatbalancingguaranteedtraf cdoesnotimprovecalls’chancesofbeingadmittedtothenetwork,nordoesitleadtohigherblockingprobabilities.

IfwenowturnourattentionontothelowerQoStraf cclass,wecantryandgaugehowthecombinationofloadbalancingappliedtobothtraf cclassescan,ontheonehand,rationalizethedistributionofguaranteedtraf c,thusfreeingupresources,and,ontheother,ef cientlyallocatetheleftoverbandwidthtobest-efforttraf c.Tothispurpose,wede nedausers’“reward”astheratiobetweenthepeakbandwidththatabest-effortcallrequestsandtheactualaveragebandwidththatthecallhasbeenabletoexploitthroughoutitslife.Figures4and5reportsuchrewards,averagedoverallcallsthatwereactivatedduringthesimulation,fordifferentvaluesoftheadmissionparameter.Itcanbeseenthatarewardincrementashighas5%canbeachievedwhentheloadbalancingalgorithmisapplied.

V.NUMERICALRESULTS

Simulationswereruntoobtainanestimateofhowmuchbandwidthcanbesparedwhentheproposedload-balancingal-gorithmisused,withrespecttoasituationwherethesamerout-Ofcourse,thisisonlyanestimateofwhatthebest-effortconnectionsget,dependingontheactualpolicyusedbythenetworktoallocateresourcestoconnections;howeverregardlessofthepoliciesandtheperformancetheyattain,therelativemeritsofroutingschemesshouldnotbeaffected.

Acloserinspectionoftheresultsallowsustolinktherewardstotheactualpathschoiceasdeterminedbytheloadbalancingalgorithm.TableIdetailstheeffectivenessoftheloadbalancingalgorithmatlimitingthenumberoftimesnon-primary(andthusmoreresourcesconsuming)pathsarecheckedforadmissionofthehigher-QoScallsbeforeasuitablepathisfoundandthecallisroutedoverit.Expressedthroughpercentages,thesequanti-tiesalsoprovideuswithageneralindicationofthecallsetuptimeandofhowitcanbeconsiderablyshortenedwhenusingaload-balancingalgorithm.

Abstract—This paper presents a load balancing method to improve network utilization when static routing algorithms are employed. Static routing algorithms can generally be reduced to a path assignment problem with the aim of minimizing a cost function: i.

5

VI.CONCLUSIONS

0.90.850.8

Users reward

0.750.70.650.61.5

no lbwith lb5 Mb/s10 Mb/s

1.61.7

Load

1.81.92

Fig.4.Averagebest-effortusers’rewardasafunctionofguaranteed-classnet-workloadinGb/s-=0.4

0.90.850.8

Users reward

0.75

no lbwith lb5 Mb/s10 Mb/s

Thispaperhaspresentedaloadbalancingpathselectionalgo-rithmforstaticroutingstrategies,thatissuitedforhierarchicalimplementationinnetworksthatsupportmultipleQoStraf c.Theloadbalancingmetricwasbasedonlyontheminimumavailablebandwidthonthepath;howevermetricsthatarebasedalsoontheexpecteddelayand/ordelayvariationsarenotdif -culttobede nedandwillbestudiedinthefuture.

Theproposedsortingalgorithmwasimplementedandasim-ulationstudywascarriedoutonacomplex,meshedtopol-ogy,withtwotraf cclasses,inordertocomparetheproposedschemewithastandardMinimum-Hoppathselectionalgorithm,applyinganuncontrolledalternateroutingstrategytothepathsselected.Resultsshowthattheproposedstrategyallowsthelowertraf cclasstoobtainanincreasedshareofresources,whileobviouslynotaffectingthehigherclasstraf c.

Thetotaltraf cadmittedwithinthenetworkwasnotobservedtochangesigni cantly;howeveritmustbenotedthatonlyasingletopologywithuniformtraf cdistributionwasstudiedinthisearlystageoftheresearchandthesituationmightchangesigni cantlyifthetraf cloadisnotuniform.Futureresearchwillcoverthispoint.

ACKNOWLEDGEMENTS

TheauthorswishtothankGabrieleFavalessaandLucaMedicofortheircontributionstothesimulatorcode.

REFERENCES

0.70.650.61.5

1.61.7

Load

1.81.92

Fig.5.Averagebest-effortusers’rewardasafunctionofguaranteed-classnet-workloadinGb/s-=1

Path#1233Path#1233

Load=1.5Unbal.Bal.98.6599.980.630.010.320.0030.400.03Load=1.8Unbal.Bal.94.0099.092.750.521.370.121.880.27

TABLEI

Load=1.6

Unbal.Bal.97.3099.911.260.040.640.010.80.04Load=2.0Unbal.Bal.90.8396.464.232.002.010.472.931.07

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