Storage device performance prediction with CART models(20)

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

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(a)Entropyplotontime(b)Entropyplotwithoperationtype

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Figure10:Entropyplotstoquantifyotherworkloadcharacteristics.

Asimilarcalculationonthetrace’s“margin”onLBNgivestheentropyplotonLBN.Figure9(b)showstheentropyplotonbotharrivaltimeandLBNofthesampletrace.

Wemaketwoobservations.First,theentropyplotshowsstronglinearity,suggestingtheskewinarrivaltimeandLBNstaysconstantatallgranularities.Theconstantincrementoftheentropyvaluefromonescaletothenextsuggeststhatthedegreeofskewstaysthesameatallthescales.Thatis,thesampletracehasthesameburstinessatallscales,whichcon rmstheself-similarityofI/Oworkloadsobservedinpreviousstudies[13].Second,thelinearentropyplotallowsustousetheentropyplotslopestocharacterizetheburstiness.Smoothtraf chasanentropyplotofslopecloseto1.Real-worldtraces,however,havestrongburstiness.Insummary,theentropyplotde nedonthetracemarginsallowsustousetwoscalarstocharacterizeboththetemporalandspatialburstinessofI/Oworkloads.

Entropyplotontwo-dimensionaldatasets.Weextendtheentropyplottohandletwo-dimensionaldatasetstomeasurethecorrelationsbetweentwoattributes.Asbefore,theentropyplotcalculatestheentropyvalueatdifferentscales,onlythistimeontwo-dimensionaldatasets.Givenatwo-dimensionalprojectionofa

2n,wedividetheprojectioninto2k2kgrids,whichaggregatesbothdimensionstrace,Cijij12

withscalek.ThisgivesaseriesCkof2k2kelements.ApplyingtheentropyfunctiontoCkgivesthejointentropyvalueatscalekonthetwodimensions.

Thejointentropyallowsustocalculatethecorrelationbetweenthetwoattributes.Thecorrelationisthedifferencebetweenthesumoftheentropyvalueonthetwoattributesandthejointentropyplot.Figure9(b)showsboththejointentropyandthecorrelationonarrivaltimeandLBNforthesampledisktrace.WeobservethatastrongcorrelationexistsbetweenarrivaltimeandLBN,andalsothatthecorrelationstaysconstantatallscales.Thus,weareabletouseascalarvalue,thecorrelationslope,toquantifythecorrelationbetweenarrivaltimeandLBN.

Entropyplotinvolvingrequestsizeandoperationtype.Itispossibletoextendtheentropyplottohandleoperationtypeandrequestsize.Theonlydifferenceisthelimitedvaluerangesofthetwoattributes,whichlimitthenumberofdatapointsintheentropyplot.Asaresult,theworkloaddescriptiondoesnotincludeentropyplotslopesonthesetwoattributes.

Quantifyingthecorrelationsinvolvingeitherofthetwoattributesfacesthesameproblem.Oursolutionistoalwaysusethe nestgranularityontherequestsizeoroperationtype,buttochangethescaleontheotherattribute.Forexample,tocalculatethejointentropyplotonarrivaltimeandrequesttype,theaggregationhappensonlyonthearrivaltime.Figure10showstheentropyplotsthatinvolveoperationtypeandrequestsize.Theseentropyplotsarenotaslinearaspreviousones.Therefore,itisnotstraightforwardtocompresseachlineintoascalar.Currently,ourworkloaddescriptionusestheaverageincrementbetweentwoadjacentscales.