An Analytical Model for Wormhole Routing with Finite Size Input Bu ers
An Analytical Model for Wormhole Routing with Finite Size Input Bu ers
An Analytical Model for Wormhole Routing with Finite Size Input Bu ers
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deadlocksarepossibleunlessadeadlock-freeroutingstrategyisemployed.Asurveyof<br />
Figure1:<strong>An</strong>illustrationofwormholerouting. beenproposedandpresentedintheliterature[7,8,9,10,11].However,theyallassumed 1.2<strong>Wormhole</strong><strong>Routing</strong><strong>An</strong>alysis Manyper<strong>for</strong>mancemodels<strong>for</strong>wormholeroutinginamulti-processorenvironmenthave<br />
wormholeroutingcanbefoundin[6].l<br />
a640MbpsMyrinet<strong>with</strong>alinklengthof25met<strong>ers</strong>needsabu<strong>ers</strong>izeofatleast54bytes propagationdelaythaninamultiprocessorinterconnectionapplication.Asanexample, toaccommodatetransitdatathatcannotbestoppedimmediatelyduetothelongerlink anegligiblesizeofinputbu<strong>ers</strong>.Thisbu<strong>ers</strong>izemustincreaseinaLANenvironment<br />
p<br />
thepossibilityofthebuerbeingemptybe<strong>for</strong>etransmissionisresumed.ALANspanning hundredsofmet<strong>ers</strong>requiresabu<strong>ers</strong>izelargerthanhundredsofbytes(abu<strong>ers</strong>izethat eectsmustbecapturedinthemodel. [2]perporttopreventdatalossduetoabueroveroworatransmissionbreakdueto monlyusedassumptionthatawormreachesitsdestinationbe<strong>for</strong>eitstailleavesitssource couldholdmorethanonepacket).Thesebu<strong>ers</strong>alleviateblockingproblem.Thus,their host,isnolongervalid.Itisnowthecasethatablockedwormmayoccupyonlyafractionofthelinksalongitspath(notallofthem).Secondly,abuermayholdmorethan<br />
one,butnotaninnitenumber,ofworms.<strong>Bu</strong>eringdelaybecomesdiculttoestimate becausethebu<strong>ers</strong>izeisnite(intermsoftheamountofdata). <strong>An</strong>itesizebuercomplicatestheanalyticalmodelintwoways.Firstly,thecom-<br />
dependencyamongalllinksisneeded.Toestimatethelinkblockingdelay,thelength ofthelinkdependencychainmustberesolvedaccordingtothewormsizedistribution. Approximations<strong>for</strong>determiningtheblockingchainlengthandthelinkblockingdelay solutionisdescribedinsection5.Theentiremodelingprocedureissummarizedinsection M/G/1/Kqueues<strong>with</strong>nitecapacity.Thestructureoftheequivalentqueueandits arepresentedinsection4.Thenitesizebuerisapproximatedthroughequivalent Todeal<strong>with</strong>thedelaycausedbyblockinginthesucceedinghops,knowledgeofthe<br />
6.Section7showscomparisonresults<strong>with</strong>simulations.Section8concludesthispaper. 2<strong>Model</strong>AssumptionsandNotation awormholeroutingnetworkusingadeadlock-freeroutingthatguaranteesnocycle Theanalysisworkpresentedinthispaperassumesthefollowings: condition<strong>for</strong>deadlockfreerouting,asdiscussedin[12,13]. oflinkdependency.Nocycleoflinkdependencyisasucient,butnotnecessary,<br />
<strong>Input</strong> Port<br />
<strong>Input</strong> buffer<br />
Cross bar<br />
Output<br />
Port<br />
(a) A wormhole routing switch<br />
p<br />
li<br />
p<br />
Λ<br />
p<br />
p i p<br />
p<br />
l i+1 l i+2 l i+3 l i+4<br />
Q Wl p Wl p Wl p Hl p Z<br />
i i+1 i+2 i+3 i+4 li+4<br />
p<br />
a worm<br />
(b) <strong>An</strong> illustration of notation and various delays
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