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A Real-Time Fault-Tolerant k-ary n-cube Multiprocessor

www.engr.newpaltz.edu/~bai eewww.eng.ohio-state.edu/~ozguner Abstract:- We present a real-time fault-tolerant design for the k-ary n-cube multiprocessor and examine its reconfigurability. The k-ary n-cube is augmented by spare nodes at stages one and two.

A Real-Time Fault-Tolerant -ary -cube Multiprocessor

BABACKIZADI

Dept.ofElect.andComp.Engineering

StateUniversityofNewYorkNewPaltz,NY12561U.S.A.

bai@engr.newpaltz.eduwww.engr.newpaltz.edu/~bai

¨¨¨FUSUNOZGUNER

Dept.ofElect.EngineeringTheOhioStateUniversityColumbus,Ohio43210U.S.A.ozguner@ee.eng.ohio-state.edueewww.eng.ohio-state.edu/~ozguner

Abstract:-Wepresentareal-timefault-tolerantdesignforthe-ary-cubemultiprocessorandexamineitsrecon gurability.The-ary-cubeisaugmentedbysparenodesatstagesoneandtwo.Weconsidertwomodesofoperations,oneunderheavycomputationorharddeadlineandtheotherunderlightcomputationorsoftdeadline.Weassumethatfaultynodescannotcompute,http://devegacer.comparedwithotherproposedschemes,ourapproachcantoleratesigni cantlymorefaultynodesandfaultylinkswithalowoverheadandnoperformancedegradation.

ary-cube,spareallocation,recon guration,augmentedmulti-Key-Words:-Faulttolerance,realtime,

processor,waveswitching,circuitswitching.

1Introduction

Inthequesttoattainpetascalecomputing,re-searchersaredesigningparallelmachineswithhun-dredsofthousandsofprocessingelements[8].The-ary-cubeisanattractivetopologytoimplementsuchparallelmachines.Anumberofmultiprocessorshavealreadybeenbuiltusingnetworksthatareeither-ary-cubeorareisomorphictoone[4,15,16].Tosustainthesamelevelofperformance,someresearchershaveinvestigatedhardwareschemesforthe-ary-cubebasedmultiprocessorswheresparenodesandsparelinksareusedtoreplacethefaultyones[3,11,12,2,1,7,5,10,17,6].Toaccommodatereal-timeappli-cations,suchfaultycomponentshavetobereplacedwithsparesinamannerthatalsosatis estherequiredcompletiondeadlineofactivetasks.Twomodesofop-erationisgenerallyconsidered:thestrictmodeandtherelaxedmode.Thestrictmodepertainstotaskswhosecomputationalrequirementsareheavyorhaveahardcompletiondeadline.Therelaxedmode,ontheotherhand,consistsoftaskswithasoftcompletiondeadlineoralightcomputationalload.Therefore,inthestrictmodeofoperation,inordertoallowforfastrecon gu-ration,sparereplacementoffaultycomponentsshouldresultinveryfewchangesinthesysteminterconnec-tions.Acommonapproachtoaccommodatethismode

ofoperationistoreplaceeachfaultycomponentwiththelocalspareusingadistributedrecon gurational-gorithm[14].Ontheotherhand,intherelaxedmodeofoperation,aglobalrecon gurationalgorithmisap-pliedtomaximizetheprobabilitythatinthenextstrictmodeofoperation,thereexistsalocalspareforeveryfaultycomponent.

Inthispaper,wepresentatwo-stageredundantschemeforthe-ary-cube.Theobjectivesoftheschemearetwofold.First,facilitatereal-timefaulttolerancebyallowingthesystemtooperateineitherthestrictmodeortherelaxedmode.Second,utilizethesparenetworktotoleratealargenumberoffacultynodesandfaultylinks.

Therestofthepaperisorganizedasfollows.Inthenextsection,notationandde nitionsthatareusedthroughoutthepaperaregiven.AnoverviewofourapproachispresentedinSection3.InSection4,weexaminetherecon gurabilityofthescheme.Boththe-oreticalandsimulationresultsarepresented.Finally,concludingremarksarediscussedinSection5.

2NotationandDe nitions

Eachnodeofa-ary-cubeisidenti edbyn-tuple

whereisaradixdigitandrep-resentsthenode’spositioninthe-thdimension.Each

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