Storage device performance prediction with CART models(4)

Storage device performance prediction is a key element of self-managed storage systems and application planning tasks, such as data assignment. This work explores the application of a machine learning tool, CART models, to storage device modeling. Our appr

usingsimulatorsisalsoresourceintensive.Analyticalmodels[7,22,24,30,31]aremorecomputationallyef cientbecausethesemodelsdescribedevicebehaviorwithasetofformulae.Findingtheformulasetrequiresdeepunderstandingoftheinteractionbetweenstoragedevicesandworkloads.Inaddition,bothdisksimulatorsandanalyticalmodelsaretightlycoupledwiththemodeleddevice.Therefore,newdevicetechnologiesmayinvalidateexistingmodelsandrequireanewroundofmodelbuilding.

OurapproachusesCART,whichtreatsstoragedevicesasblackboxes.Asaresult,themodelconstruc-tionalgorithmisfullyautomatedandshouldbegeneralenoughtohandleanytypeofstoragedevice.Thedegenerateformsof“black-boxmodels”areperformancespeci cations,suchasthemaximumthroughputofthedevices,publishedbydevicemanufacturers.Theactualperformance,however,willbenowherenearthesenumbersundersomeworkloads.Anderson’s“table-based”approach[3]includesworkloadcharacter-isticsinthemodelinput.Thetable-basedmodelsrememberdevicebehaviorforawiderangeofworkloadanddevicepairsandinterploatesamongtablesentriesinpredicting.Anderson’smodelsareusedinanautomatedstorageprovisiontool,Ergastulum[2],whichformulatesautomaticstorageinfrastructureprovi-sioningasanoptimizationproblemandusesdevicemodelstoguidethesearchalgorithminlocatingthesolution.Ourapproachimprovesonthetable-basedmodelsbyemployingmachinelearningtoolstocapturedevicebehavior.Becauseofthegoodscalabilityofthetoolstohighdimensionaldatasets,weareabletousemoresophisticatedworkloadcharacteristicsasthemodelinput.Asaresult,themodelsaremoreef cientinbothcomputationandstorage.

Workloadcharacterizationisanimportantpartofdevicemodelingbecauseitprovidesasuitablerep-resentationofworkloads.Despiteabundantpublishedworkinmodelingwebtraf c[23,25,8],I/Otraf cmodelingreceiveslessattention.Directapplicationofwebtraf canalysismethodstoI/worktraf chasacategoricaladdressspace,andthereisnonotionofsequentialscans.Incontrast,theperformancevariabilitycanbeseveralordersofmagnitudebetweenrandomandsequentialaccessesforI/Oworkloads.Ganger[10]pointedoutthecomplexityofI/Oworkloads,andeventhedetectionofsequentialscansisahardproblem[19].Gomezetal.[14]identi edself-similarityinI/Otraf candadoptedstructuralmodelstogenerateI/Oworkloads.Kurmasetal.[20]employedaniterativeapproachtodetectimportantworkloadcharacteristics.Rome[34]providedageneralframeworkofworkloadspeci cations.Alltheapproaches,inonewayoranother,useempiricaldistribu-tionsderivedfromgivenworkloadsastheparametervalues.Ourpreviouswork[32]takesadvantageoftheself-similarityofI/Oworkloadsandproposesatool,the“entropyplot,”tocharacterizethespatio-temporalcharacteristicsofI/Oworkloadswiththreescalars.SinceourCART-basedmodelsrequireworkloadstobepresentedintheformofvectorsofscalars,theentropyplotisanattractivechoice.

3Background:CARTModels

ThissectiongivesabriefintroductionoftheCARTmodelsandjusti esourchoiceofthetool.AdetaileddiscussionofCARTisavailablein[4].

3.1CARTModels

CARTmodelingisamachinelearningtoolthatcanapproximaterealfunctionsinmulti-dimensionalCarte-fXε,sianspace.(Itcanalsobethoughtofasatypeofnon-linearregression.)GivenafunctionY

dwhereX ,Y ,andεiszero-meannoise,aCARTmodelapproximatesYusingapiece-wiseconstant f X.WerefertothecomponentsofXasfeaturesinthefollowingtext.Theterm,ε,capturesfunction,Y

theintrinsicrandomnessofthedataandthevariabilitycontributedbytheunobservablevariables.Thevari-anceofthenoisecouldbedependentonX.Forexample,thevarianceofresponsetimeoftendependsonthearrivalrate.