DTIC ADA440180: Investigating the Effect of Voltage-Switching on Low-Energy Task Scheduling in Hard Real-Time Systems

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Investigating the Effect of Voltage-Switching on Low-Energy Task Scheduling in
Hard Real-Time Systems
1
VishnuSwaminathanandKrishnenduChakrabarty
Dept. ofElectrical&ComputerEngineering,Duke University
Durham,NC 27708,USA
vishnus,krish @ee.duke.edu
f g
Abstract a number of these methods are aimed at the synthesis of
low-power designs and they do not address energy mini-
Weinvestigatetheeffectofvoltage-switchingontaskex- mizationduringfieldoperation.
ecutiontimesandenergyconsumptionfordual-speedhard Inthispaper,wepresentanon-lineschedulingalgorithm
real-timesystems,andpresentanewapproachforschedul- forreal-timesystemsthatattemptstominimizetheenergy
ingworkloadscontainingperiodictasks. Ourmethodmin- consumedbyaperiodictasksetwhilealsoconsideringthe
imizesthetotalenergyconsumedbythetasksetandguar- voltage switching times and energies. The algorithm is
antees that the deadline for every task is met. We present based on the well-known earliest-deadline-first (EDF) al-
a mixed-integer linear programming model for the NP- gorithm [9, 7]. We consider a practical scenario where
complete scheduling problem and solve it for moderate- a single CPU executes a set of periodic non-preemptable
sizedprobleminstancesusingapublic-domainsolver. For tasks. The voltage, and consequently the clock speed, of
larger task sets, we present a novel extended-low-energy theCPUmaybeswitchedbetweentwoormorevaluesdy-
earliest-deadline-first(E-LEDF)schedulingalgorithmand namicallyatrun-timethroughOSsystemcalls.Thisoption
applyittotworeal-lifetasksets. Ourresultsshowthaten- is available in most modern computers, which provide at
ergycanbeconservedinembeddedreal-timesystemsusing least two different operating speeds [5]. Unlike previous
energy-awaretaskscheduling.Wealsoshowthatswitching approaches,e.g. [4],wemaketherealisticassumptionthat
times have a significant effect on the energy consumed in voltageswitchingtakestimeandconsumesenergy. During
hardreal-timesystems. this switching period, the CPU cannot execute any tasks.
We attemptto findthe voltage at whicheach task must be
executed such that the energy consumed by the entire set
1 Introduction
ofperiodictasksis minimizedandgeneratea schedulefor
In embedded systems with variable-speed processors, thetasksetsuchthatthereleasetimerequirementsaresat-
isfied and the deadlines for every task is met, while also
the operating system (OS) can reduce energy consump-
accountingfortheeffectofthevoltageswitchingtimeson
tion by scheduling tasks appropriately. For real-time sys-
tems, optimal preemptive off-line scheduling algorithms theenergyconsumptionofthetaskset.
havebeendeveloped[16]. Heuristics foroff-lineschedul-
2 Preliminaries
ingofnon-preemptivereal-timetaskswerepresentedin[4].
On-lineandoff-lineschedulingalgorithmsforthepreemp- In this section, we present our notation and the under-
tivetaskmodelhavealsobeendeveloped[6,11]. Fromthe lying assumptions. We are given a set of periodic tasks
hardwareperspective,researchershavedevelopedefficient . Eachtask hnasthefollowing
DC-DCswitchingconvertersthatallowthesupplyvoltage Rpar=amfert1e;rsr:2;a::re:l;eransge (or arrival)rtiim2eR , a deadline , a
toberapidlychangedunderexternalcontrol[10].Although length (representedinnumberofinstrauictioncycles),daind
theschedulingmethodscitedaboveareveryefficient,most aperiodli .
of themmake the assumptionthat the CPU can operateat Eachtpaisk isreleasedattime .Weassume,with-
several different voltage levels (and hence different clock outloss of gernierality,that all taskts=haavie identicalperiods.
frequencies)whichcanbevariedcontinuously.Inaddition, Alltasksmustcompleteexecutionbeforetheirdeadlines.
WeassumethattheCPUcanoperateatoneoftwovolt-
This research was supported in part by DARPA under grant no.
1 ages: or . Dependingon the voltage level, the CPU
N66001-001-8946, andinpart byagraduate fellowship fromtheNorth
CarolinaNetworkingInitiative. speedVm1aytaVk2eontwovalues: or . Themodelcanbe
s1 s2
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Investigating the Effect of Voltage-Switching on Low-Energy Task
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Scheduling in Hard Real-Time Systems
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unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
easilyextendedtohandlemorethantwovoltages(speeds). proportionalto ,wehave: 2 2 2.
2 2 xi s1 s2
ThesupplyvoltagetotheCPUisunderOScontrolandthe We next moxdeil the requirveim=en(cid:11)t2th=ataaill(cid:1)t(cid:11)a2sk+dbeiad(cid:1)l(cid:11)in2es
OS may dynamically switch the voltage during run-time. must be met. This is ensured by introducing completion
Werestrictourselvestotwospeedsoutofpracticalconsid- time variables , where is the time
li
erations. CPUspeedsarespecifiedintermsofthenumber takentoperformcia=votlita+gexsiw+itcths,sawnid istasbinaryvari-
of instructions executed per second. Each task may be able whose value is if a switch ocscwurired immediately
executed at a voltage , , and corrirespond- before task . We h1ence obtain the following inequal-
ingly,ataspeed , vi vi 2 .fVT1h;eVv2goltage(speed)may ity: r.iThe above inequalities are non-linear. The
beswitchedtoadxiiffexrien2tvsa1l;use2betweentasks. Thesystem non-lciine(cid:20)aridtiiesmaybeeliminatedusingstandardtechniques
uses unitsofenergyand unitsoftimeinperforminga [15].
voltagCeswitch. ts Non-concurrencyoftasksmaybemodeledwiththefol-
Itiswell-knownthatpowerconsumptioninCMOScir- lowinginequalities:
cuits has a quadratic dependence on the CPU voltage.
Hence, energy consumed by task of length is
given by E2i , and the total energryi consumed floir a ti(cid:0)tj(cid:0) lj (cid:21)0ortj(cid:0)ti(cid:0) li (cid:21)0; 1(cid:20)i;j (cid:20)n;i6=j:
given taskEsiet/isvpirloiportionalto . In the subse- xj xi
n 2
quent dicussion, we measure enePrgyi=c1ovnisluimptionin units Thisrepresentsthefactthatwhentask hasbeensched-
uledtostartexecutionat time ,nootherritask canstart
of .
PAlnit=ho1uvgi2hlitheschedulingproblemisNP-complete,itcan executionuntil hascompletetdi. rj
Theaboveinreiqualityisnon-lineartoo.Thismaybealso
besolvedexactlyformoderate-sizedinstancesusingmixed-
belinearizedusingstandardlinearizationtechniques.These
integer linear programming(MILP). In the following sec-
techniquesarenotexplainedhereduetospacelimitations.
tion,wepresentanMILPmodelforthelow-energyschedul-
Finally,wemodelthefactthatatask startsassoonas
ingproblemwithswitchingtimesandenergies.
aprevioustask ends.Thisisdonebyirnitroducinginteger
3 Mixed-integer linearprogrammingmodel variables rajnd through .
zeroi (cid:12)i1 (cid:12)in
ThegoalofMILPistominimizealinearobjectivefunc-
tiononasetofintegerand/orrealvariables,whilesatisfying zeroi((cid:12)i1(ti(cid:0)c1)+(cid:12)i2(ti(cid:0)c2)+:::+(cid:12)in(ti(cid:0)cn))=0:
The final MILP model is shownin Figure 1. Although
asetoflinearconstraints.
theMILPmodelistoocomputationally-intensivetobeused
Theoptimizationproblemweaddressistominimizethe
forlargetasksets,itishelpfulindeterminingalowerbound
totalenergyconsumedbythesetof tasksbyoptimallyde-
terminingtheirstarttimes n ,theirvoltagesand ontheamountofenergyconsumedbya giventaskset. In
correspondingexecutionspte1e;dts2.;:::;tn theMILPformulationdescribedabove,aprioriknowledge
of the release times has been inherentlyassumed. We ob-
Thefollowingconstraintsneedto bemodeled: (i)CPU
serve that energy can be minimized to a greater extent in
speeds are limited to one oftwo values— or , (ii) the
deadlineforeachtaskmustbemet,(iii)resa1l-timse2tasksare the off-linecase thanin theon-lineone. This justifies use
ofMILPas a comparisontool forprovidinglowerbounds
non-preemptable,(iv)ataskmaystartonlyafterithasbeen
onenergyconsumption. In the nextsection, we providea
released,and(v)tasksimmediatelyfolloweachother.
descriptionofourheuristicandourexperimentalresults.
We observedin Section 2 that the energyconsumedby
task is . Moreover, with each task is 4 The E-LEDF heuristic
2
an asrsiociatEedi s/witcvhiilnig cost if a voltage switchrwi as
performed immediately beforeCtihe task began execution. AlthoughMILPisausefulandoptimalsolutionmethod
forsmallprobleminstances,itcannotbeusedforlargetest
Hence,tominimizeenergy,we needtominimizetheterm
cases. In order to solve large problem instances, we have
,andthisisnowourobjectivefunction.
2
P(Wlievia+ssuCmi)e a linear relationship between the operating developedaheuristicalgorithmtogeneratenear-optimalso-
lutionsinpolynomialtime.
voltage ofthe processorand its executionspeed . This
generallvyholds true for processors designed usingxCMOS The extended-low-energy earliest deadline first heuris-
tic, or simply E-LEDF, is an extension of the well-known
technology[13].Hence, .
xi earliest deadline first (EDF) algorithm. The operation of
vi =
First, weintroducebinaryv(cid:11)ariables and torestrict E-LEDFisdescribedinFigure2.
,theexecutionspeedoftask ,tobeeaiither bior . The ToillustratetheeffectivenessofE-LEDF,wealsodevel-
xfoillowing constraints relate iand to : s1 s2 opedasimplelow-energyearliestdeadlinefirstalgorithm
,and . ai bi xi xi = ais1 + (LEDF) [14] that does not take into account the effect of
bisS2ince aim+abyib=ew1rittenintermsof and ,and is voltageswitching.LEDFgeneratednear-optimalschedules
2
xi s1 s2 vi
ProcedureE-LEDF()
Minimizethecostfunction 2 subjectto: begin
1. 2 2Plivi +Ci,swi Repeatforever
2. vi2 =ai(cid:1) (cid:11)s12 +bi(cid:1) (cid:11)s22;1,(cid:20)i(cid:20)n Rememberspeedatwhichprevioustaskwasscheduled
3. ai+bi=1; 1(cid:20)i(cid:20)n , iftasksarewaitingtobescheduledinreadylistthen
4. (cid:14)ij1+(cid:14)ij2 =1; 1(cid:20)i;j (cid:20)n;i6=j , Sortdeadlinesinascendingorder;Selecttask withearliestdeadline
5. ci =ti+ui+tssw,i; 1(cid:20)i;j (cid:20)n;i6=j ifthisisthefirsttasktobescheduledthen ri
6. ci (cid:20)di; 1(cid:20)i(cid:20)n , If ,scheduletaskatlowervoltage(speed);continue
7. xi=ais1+bis2; 1(cid:20)i(cid:20), n Iftlow+ts(cid:20)d,ischeduletaskathighervoltage(speed);continue
8. vi(cid:0)liai (cid:20)0; 1(cid:20)i(cid:20)n, Catlhlie+xcetpsti(cid:20)ondhiandler!!
9. (cid:0)ui+vi (cid:20)0; 1(cid:20)i(cid:20)n , else
10. ui(cid:0)vi+liai(cid:20)li; 1(cid:20)i,(cid:20)n ifpreviousspeed=highspeedthen
11. wi(cid:0)libi (cid:20)0; 1(cid:20)i(cid:20)n, Compute and
12. (cid:0)ui+wi(cid:20)0; 1(cid:20)i(cid:20)n , iftaskisnEohtischeduElalobwlethen
13. ui(cid:0)wi+libi (cid:20)li; 1(cid:20)i(cid:20)n Callexceptionhandler!!
fij1i(cid:0)fij1j(cid:0)eij1j(cid:0)ds,ij1j+fij2j(cid:0)fij2i(cid:0)eij2i(cid:0)dsij2j (cid:21) else
14. 0; 1(cid:20)i;j (cid:20)n;i6=j , if
15. (cid:13)1ij+(cid:13)2ij =1; 1(cid:20)i;j (cid:20)n;,i6=j itflow+ts(cid:20)dithen
16. fij1i(cid:0)di(cid:14)ij1 (cid:20)0; 1(cid:20)i(cid:20),n IEflow(cid:20)Ehi ,scheduletaskatlowspeed
17. (cid:0)ti+fij1i (cid:20)0; 1(cid:20)i(cid:20)n , elsetlow+ts(cid:20)di
18. ti(cid:0)fij1i+di(cid:14)ij1 (cid:20)di; 1(cid:20)i(cid:20)n, If ,scheduleathighspeed
19. eij1i(cid:0)li(cid:20)0; 1(cid:20)i;j (cid:20)n;i6=j , else thigh+ts(cid:20)di
20. (cid:0)ui+eij1i (cid:20)0; 1(cid:20)i;j (cid:20)n;i6=j , Scheduletaskathighspeed
21. ui(cid:0)eij1i+li(cid:14)ij1 (cid:20)li; 1(cid:20)i,;j (cid:20)n;i6=j ifpreviousspeed=lowspeedthen
22. fij2i(cid:0)di(cid:14)ij2 (cid:20)0; 1(cid:20)i(cid:20),n Compute and
23. (cid:0)ti+fij2i (cid:20)0; 1(cid:20)i(cid:20)n , iftaskisnEohtischeduElalobwlethen
24. ti(cid:0)fij2i+di(cid:14)ij2 (cid:20)di; 1(cid:20)i(cid:20)n, Callexceptionhandler!!
25. eij2i(cid:0)li(cid:20)0; 1(cid:20)i;j (cid:20)n;i6=j ,and else
26. (cid:0)ui+eij2i (cid:20)0; 1(cid:20)i;j (cid:20)n;i6=j . if then
27. ui(cid:0)eij2i+li(cid:14)ij2 (cid:20)li; 1(cid:20)i;j (cid:20)n;i6=j , itfhi+ts(cid:20)di then
28. swi=Pjfolij(aibj+ajbi); 1(cid:20)i;j (cid:20)n;ineqj, SEchhied(cid:20)ulEeltoawskathighspeed
29. folijabsij(cid:0)folij (cid:20)absij(cid:0)1; 1,(cid:20)i;j (cid:20)n;i6=j else
30. Pjfolij (cid:20)1; 1(cid:20)i;j (cid:20)n;i6=j , If ,scheduletaskatlowspeed
31. absij =(cid:13)1ij(ti(cid:0)cj)+(cid:13)2ij(cj(cid:0)ti) , end tlow+ts(cid:20)di
32. folijabsij(cid:0)folij (cid:20)absij; 1(cid:20)i;j, (cid:20)n;ineqj Figure2.PseudocodefortheE-LEDFalgorithm.
33. folijabsij =0; 1(cid:20)i;j (cid:20)n;i6=j speedsaredynamicallyswitchable. Wehavealsoassumed
zeroi((cid:12)i1(ti(cid:0)c1)+(cid:12),i2(ti(cid:0)c2)+:::+(cid:12)in(ti(cid:0)cn))= thattheCPUoperatesat200MHzat3.3Vandat100MHz
34. 0; 1(cid:20)i;j (cid:20)n;i6=j ,
35. (cid:12)i1+(cid:12)i2+:::(cid:12)in =1; 1(cid:20)i(cid:20),n at1.65V.Furthermore,inordertoemphasizeenergymin-
zeroiti+zeroi (cid:21)ti; 1(cid:20)i(cid:20)n imization, the deadlines we have used are tighter than the
Figure1.Mixed-integerlinearprogrammingmodel. actualdeadlinesforthe actualtaskset. Theminimumand
foranumberoftasksets;henceitwasusedforcomparison maximum voltage-switchingtimes were chosen to be 1
purposes. unitand5units,respectively,andthtes minimumandmaxi-
mum voltage-switchingenergies were chosen to be 10
WeranLEDFandE-LEDFontasksetscomprisingthir-
unitsand200units,respectively[E10s]. Thesenumbershave
teentoseventeentasks[14]. We showaplotoftheenergy
been chosen because the DC-DC switching converter de-
consumedfor3differentschedulingstrategiesinFigure3.
scribed in [10] has a switching time of less than 6 units.
Weobservethattheenergiesconsumedinschedulesgen-
TheLEDFandE-LEDFresultsareshowninTable1.
erated by E-LEDF are greater than that of the MILP and
LEDF schedules. Our results show that voltage-switching
Taskset Configuration LEDF E-LEDF increase
timesandvoltageswitchingenergiesplayasignificantrole =5, =200 213376.26 %6.99
in the energyconsumptionof a real-time system, with the 24tasks ts =5,vs =10 199418.76 212236.26 6.42%
energyrisingbyasmuchas . (Avionics) ts=1, vs=200 201771.65 1.17%
We next consider two rea1l6-%life task sets comprising 24 ts =1,vs =10 200631.65 0.60%
ts=5, vs=200 380317.625 22.90%
and39tasks,respectively. Thesetasksetswereusedinthe 39tasks ts =5,vs =10 309338.65 378987.625 22.50%
developmentofanapplication-specificintegratedcircuitfor (ASW) ts=1, vs=200 345221.25 11.59%
anavionicsapplication[12]andinanembeddedsignalpro- ts =1,vs =10 342751.25 10.80%
ts vs %
cessing application for an anti-submarine warfare (ASW)
Table1.Resultsfortworeal-lifetasksets.
system [1]. For the set of 24 tasks, we assume the pro-
cessor speeds to be 100 MIPS and 260 MIPS, with corre- We seefromTable1thatvoltageswitchingenergiesdo
spondingvoltages1.2Vand3.3Vrespectively.Inthecase nothaveassignificantaneffectasvoltageswitchingtimes
oftheset of 39tasks, we have assumedthat theprocessor on the energyconsumptionof the task set. This is due to
is capableofoperatingat 100MHz andthat theprocessor the fact that voltage switching energies do not affect the
x 105 timetasksets,andshowedthatouralgorithmprovidesnear-
1.9
optimalsolutions.
1.8
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