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.