Specification and management of QoS in real-time databases s(5)

comparedtomO

r,mdeissettoalowvaluerelativetomder.AsmOMAincreases,mdeisincreased,buttoamaximumvalueofmderÂðMpþ100ÞsinceafurtherincreaseviolatesthegivenQoSspecification.TheoutlineofPC-MPisgiveninFig.2b.

IEEETRANSACTIONSONCOMPUTERS,VOL.55,NO.3,MARCH

2006

PC-ATEHEFandPC-ATEHEDF.ThesealgorithmsaretwovariantsofPC-MP,butwhereQoTismeasuredintermsofate,insteadofmO.Hence,wereplacethemisspercentagecontrolloopsforasingleaveragetransactionerrorcontrolloop.Here,mdeisadjustedbasedonthecontrolsignal lERandthemovingaverageofate,denotedateMAðkÞ.WedonotprovidefullalgorithmdescriptionsforPC-ATEHEFandPC-ATEHEDF,butreferinsteadtoFig.2b,wheremOMAisreplacedwithateMA.

TheprecisionofthedataiscontrolledbytheQoDmanagerbysettingmdedependingonthesystembehavior.Whenfisusedtocomputemdeðkþ1Þbasedon lERðkÞ,thefollowingschemeisused:DiscardinganupdateresultsinadecreaseinCPUload,whichwerefertoasthegainedload.Let

glðkÞ¼1

XTeeti

Ti

2discardedðkÞ

bethesumoftheestimatedexecutiontimeofthediscardedupdatetransactionsdividedbythesamplingperiodT,wherediscardedðkÞisthesetofdiscardedupdatetransac-tionsandeetiistheestimatedexecutiontimeoftheupdatetransactionTi.Inourapproach,weprofilethesystemandmeasureglforvaryingmdeandlinearizetherelationshipbetweenthem.Duringeachmonitoredand ðkÞ¼mdeðkÞ

samplingperiod,glðkÞis

kÞarecomputed.Consequently,anditsmovingaverageMAðtherelationbetweenmdeandglisupdatedtocapturethecurrentstateofthesystem.Havingtherelationshipbetweenglandmde,weintroducethehelpfunction,

hð lERðkÞÞ¼minð MAðkÞÂðglðkÞÀ lERðkÞÞ;

mderÂðMpþ100ÞÁ

:

SincemdeisnotallowedtoovershootmorethanmderÂðMpþ100Þ,weusetheminoperatortoenforcethisrequirement.Further,sincemdebydefinitioncannotbelessthanzero,weapplythemaxoperatoronhandobtainmdeðkþ1Þ¼fð lERðkÞÞ¼maxðhð lERðkÞÞ;0Þ.

4.6SystemModeling

Totunefeedbackcontrollersthatareefficientinmanagingthedesiredperformanceandthatreactrapidlytochangesinworkload,itisnecessarytohaveamodelthataccuratelydescribesthebehaviorofthecontrolledsystem[14].Theparticularformofthemodelsweconstruct,i.e.,linearmodels,enablesustouseasetofpowerfulanalyticalmethodsthatareavailableincontroltheory,e.g.,rootlocus[14].Foranalysispurposes,weapplytheprinciplesofZ-transformtheory[14].UsingZ-transformsenablesustoreducethecomplexityoflargedynamicsystemsintothesimplerrepresentationbyZ-transforms.Further,Z-transformsareusedinmanycontrollertuningprocedures,e.g.,rootlocus[14].Weadoptthefollowingnotation,whereAðzÞdenotestheZ-transformofthevariableaðkÞ.Thegoalistoderiveatransferfunctiondescribingtherelationbetweenthemanipulatedvariable,i.e.,ÁLERðzÞ,andthecontrolledvariables,i.e.,MMðzÞ,MOðzÞ,ATEðzÞ,andUðzÞ.Inthissection,wefirstpresenttheSTAmodel,previouslypresented[11],wheresomedynamicrelationsareapproximatedbystaticrelations(hence,thenameSTAreferringtoThen,wepropose

Abstract—Real-time applications such as e-commerce, flight control, chemical and nuclear control, and telecommunication are becoming increasingly sophisticated in their data needs, resulting in greater demands for real-time data services that are provided

AMIRIJOOETAL.:SPECIFICATIONANDMANAGEMENTOFQOSINREAL-TIMEDATABASESSUPPORTINGIMPRECISECOMPUTATIONS311

anewmodel,calledDYN,whichgeneralizestheSTAmodel[11]bycapturingadditionalsystemdynamics(thenameDYNrefersto4.6.1STA

TheestimatedrequestedworkloadofadmittedusertransactionslERinthenextsamplingperiodischangedthroughthemanipulatedvariable lER,givenby

lERðkþ1Þ¼lERðkÞþ lERðkÞ:

ð1Þ

Hence,lERistheintegrationofthecontrolinput lER.Now,theestimatedadmittedworkloadofusertransactionslEmaydifferfromlERsinceexternalloadappliedonthedatabasemaynotbesufficienttosatisfylERortheadmittedworkloadisdecreasedduetodeadlinemissesand,consequently,earlyterminationoftransactions.Here,however,weapproximatetheestimatedloadofadmittedtransactionsbylER,i.e.,lE¼lER(inDYN,wetakeadifferentapproach).

Theactualworkload,denotedlAðkÞ,maydifferfromlEðkÞduetoincompleteknowledgeaboutthecontrolledsystem,e.g.,unknownexecutiontimesofthetransactionsanddataconflicts.Therefore,wegetlAðkÞ¼gAðkÞlEðkÞ,wheretheworkloadratiogAðkÞrepresentstheworkloadvariationintermsofactualtotalrequestedworkload.Forexample,gAðkÞequaltotwomeansthattheactualworkloadistwicetheestimatedworkload.Itis3obviousthatgAðkÞcannotbedeterministicallymodeled.However,byprofil-ingthecontrolledsystem,wecancomputegAðkÞforeachsamplingandformtheaverageofgAðkÞ,denotedgA,whichisthenusedinourmodeltodescribetherelationbetweenlEandlAintheaveragecase,i.e.,

lAðkÞ¼gAlEðkÞ:

ð2Þ

TherelationshipbetweentheactualworkloadlAandthe

utilizationuisnonlinearduetosaturation,asgivenbythefollowing:

uðkÞ¼&

lAðkÞ;lAðkÞ 100%

100%;lAðkÞ>100%:ð3Þ

WhenlAðkÞislessthanorequalto100percent,i.e.,theCPUisunderutilized,uðkÞisoutsideitssaturationzoneandequalslAðkÞ.However,whenuðkÞiswithinitssaturationzone,i.e.,lAðkÞisgreaterthan100percent,thenuðkÞremainsat100percent,despitechangestolA.

Fromclassicalschedulingtheory,itispossibletodeterminewhetherasetoftaskscanbescheduledsuchthatnodeadlinemissesoccur[8].Turningtothecaseofthemisspercentages,wedefinetheschedulablethresholdformandatorysubtransactions,denotedlMt …… 此处隐藏：4752字，全部文档内容请下载后查看。喜欢就下载吧 ……