QoS-aware routing schemes based on hierarchical load-balanci(2)

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.

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