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