Specification and management of QoS in real-time databases s(6)

gateate¼

;ate¼ate6Þ

A

r:

ðFrom(1)-(6),wecanderiveatransferfunctionforeachofthecontrolledvariableswhentheyareoutsidetheirsaturationzones.Hence,undertheconditionlA 100%,

thereexistsatransferfunctionGSTA;UðzÞ¼gA

inputÁLUðzÞfromthecontrolERðzÞtoCPUutilization.Similarly,

undertheconditionslMthðkÞ<lA,lOtransferfunctionsthðkÞ<lA,andlate

thðkÞ<lA,theGM¼

AgMmzÀ1;GOgAgOgAgSTA;mðzÞ

gSTA;mðzÞ¼m

zÀ1;GSTA;ateðzÞ¼atezÀ1

relatethecontrolinputÁLERðzÞtothecontrolledvariables

MMðzÞ,MOðzÞ,andATEðzÞ,respectively.

4.6.2DYN

InDYN,weextendthemodelSTAtoincludeadditionalsystemdynamics.InSTA,weassumedthattherearestaticrelationsbetweenlER,u,mM,mO,andate.Wehereshowthat,infact,therearedynamicrelationsbetweenthesevariablesandSTAfailstocapturethem.Startingfromthemodelinput lERðkÞ,wecomputelERðkÞaccordingto(1).

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

312GivenacertainlERðkÞ,theestimatedworkloadofadmittedusertransactions,

lEðkÞ¼gLminðlERðkÞ;l"EðkÞÞ;

ð7Þ

istheproductoftherequestedloadfactorgLandthe

minimumoftheestimated"requestedloadandthemaximumestimatedloadlEðkÞthatcanbemadeavailable.Theupperlimitoftheadmittedload,givenbyl"EðkÞ,makestherelationshipbetweenlERðkÞandlEðkÞnonlinearduetosaturation.lEðkÞbecomessaturatedwhenitiswithinitssaturationzone,givenbylER>l"EðkÞ.However,whenoutsidethesaturationzone,lEðkÞincreaseslinearlywithlERðkÞ.Furthermore,eventhoughoutsidethesaturationzone,theestimatedadmittedworkloadlEðkÞmaybelowerthantheestimatedrequestedworkloadlERðkÞduetoearlyterminationofthetaskscausedbydeadlinemisses.Tocapturethisdifference,wederivetheratiobetweenlERðkÞandlEðkÞinthevicinityoflEðkÞcorrespondingtomOweobtainrequestedloadfactorgroraterandL.Now,undertheconditionlER<l"E,itcanbeobservedthat,givenacertainincreaseinestimatedrequestedworkloadlER,ittakessometimebeforetheestimatedloadlEand,hence,theutilizationureachlER.ThetimeittakesforlEtoreachlERisdeterminedbytheamountofworkloadsubmittedtothesysteml"Eor,morespecifically,thearrivalrateofthetransactionssubmittedtothesystem.Thegreaterl"Eis,thefasterwecanfilluptheworkload,reachinglERearlier.Similarly,adecreaseinlERdoesnotresultinanimmediatedecreaseinlEsincecurrentlyrunningtransac-tionshavetoterminate.Hence,anincrease/decreaseinlERdoesnotresultinanimmediateincrease/decreaseinlEand,consequently,wehaveadynamicrelationbetweenlERandlE.TherelationbetweenlEandlAislinearizedaccordingto(2),i.e.,wedescribetheactualworkloadintermsgA.

Furthermore,wearguethattherelationbetweenlAandmM

,mO,ateisnonstatic.WegivetherationaleonlyforthecaseoflAandamissratiom,asthedynamicsoftherelationshipbetweenlAandateisdescribedbythesamelineofargument.GivenacertainlA,thetimeittakesformtoreachgmlA,shownin(4),dependsontheactualbasicschedulerused.UnderEDFscheduling,newlyadmittedtransactionsareplacedfurtherdowninthereadyqueuesincetheyarelesslikelytohaveearlierdeadlinesthantransactionsadmittedearlier.Thismeansthatanactualchangetomisnotnoticeduntilthenewlyadmittedtransactionsareexecuting,whichmaytakeawhileuntiltheolderoneshaveterminated.ConsidertheexamplegiveninFig.3,wheretheexecutiontimeofthetransactionsistwotimeunits.Wewanttoincreasethenumberofdeadlinemissesduringinterval½kT;ðkþ1ÞT and,hence,atsam-plingk,weincreasetheloadbyraisingtheadmissionrateoftransactions,whicharescheduledtobeexecutedlaterthanthealreadyadmittedtransactions,i.e.,ininterval½ðkþ1ÞT;ðkþ2ÞT .AsshowninFig.3,thenumberofdeadlinemissesdoesnotincreaseintheinterval½kT;ðkþ1ÞT ,insteaditincreasesintheinterval½ðkþ1ÞT;ðkþ2ÞT ,whichcausesadelaybetweentheissuingofloadincreaseandtheobservedincreaseinnumberofdeadlinemisses.UnderHEFscheduling,newly

IEEETRANSACTIONSONCOMPUTERS,VOL.55,NO.3,MARCH

2006

Fig.3.AchangetolAisnotnoticedimmediatelywhenEDFisapplied.

arrivedtransactionsaremorelikelytohavehigherprioritythanoldtransactions(sincetheyhavegreatertransactionerror)and,hence,theyareplacedatthefrontofthereadyqueue.Thesetofnewlyadmittedtransactionsarethereforeexecutedinstantaneouslyand,hence,achangetomisnoticedearlierthancomparedtoEDFscheduling.Hence,underHEFscheduling,thecontrolledvariableismoreresponsivetochangesinthemanipulatedvariableasmconvergesfastertowardgmlA.

Wehavenowestablishedthat,givenacertainchangeinlER,ittakessometimebeforethecontrolledvariablesu,

mM,mO,andatereachtheirfinalvaluesuS,mMS,mO

S,andateSinthesteady-state.Thespeedbywhichacontrolledvariablereachesitsfinalvaluesisdeterminedbythetimeconstantofthesystem.LetTdenotethesamplingperiod,

andTu,TOm

M,TmO,andTatedenotethetimeconstantsofu,mM,m,andate,respectively.Togiveaconcisestatementofthemodeling,weonlyexaminethecaseformMasthedynamicsofu,mO,andatearemodeledsimilarly.Thedifferenceequation,

mM

ðkþ1Þ¼TðmMSðkÞÀmM

ðkÞÞTþmMðkÞ;ð8Þ

mrelatesmManditsfinalvaluemMSsuchthatittakesa

numberofsamplesformMtoreachmMS.Initially,whenthe

differencebetweenmMSandm

M

islarge,mMconvergesrapidlytowardmMS.However,thespeedofconvergence

decreasesasthedifferencebetweenmMSandm

M

decreases.Itshowsthatthesp …… 此处隐藏：4322字，全部文档内容请下载后查看。喜欢就下载吧 ……