Power-Aware Task Motion for Enhancing Dynamic Range of Embedded Systems with Renewable Energy Sources

Transcription

1 Power-Awre Tsk Motion for Enhning Dnmi Rnge of Emedded Sstems with Renewle Energ Soures Jinfeng Liu, Pi H. Chou, nd Nder Bgherzdeh Deprtment of Eletril nd Computer Engineering, Universit of Cliforni, Irvine, CA , USA {jinfengl, hou, Astrt. New emedded sstems re eing uilt with new tpes of energ soures, inluding solr pnels nd energ svenging devies, in order to mimize their utilit when tter or A/C power is unville. The lrge dnmi rnge of these unsted energ soures is giving rise to new lss of power-wre sstems. The re similr to low-power sstems when energ is sre; ut when energ is undnt, the must e le to deliver high performne nd full eploit the ville power. To hieve the wide dnmi rnge of power/performne trde-offs, we propose new tsk motion tehnique, whih tunes the sstem-level prllelism to the power/timing onstrints s n effetive w to optimize power utilit. Results on rel-life emples show n energ redution of 24% with 49% speedup over est previous results on the entire sstem. Kewords: power-wre sheduling/tsk motion, timing/power onstrint modeling, power/performne rnge, sstem-level design 1 Introdution Reent ers hve seen the emergene of power-wre emedded sstems. The re hrterized not onl low power onsumption, ut more generll their ilit to support wide rnge of power/performne trde-offs. Tht is, these sstems n e viewed s providing knos tht n e turned one diretion to redue power onsumption, or the other diretion to inrese performne. The ilit to dpt the rnge of power/performne trde-offs is driven new pplitions tht demnd ver high performne while under stringent timing nd power onstrints. One emple tht fits this desription is the Mrs rover NASA/JPL [1]. It ws designed to rom on Mrs to tke digitl photogrphs nd perform sientifi eperiments over severl hundred ds. Its energ soures onsist of tter pk nd solr pnel, nd future versions re epeted to inorporte nuler genertors, therml tteries, nd energ svenging devies. Besides the Mrs rover, mn new emerging emedded sstems re lso following this trend towrds new tpes of heterogeneous, renewle energ soures. Future personl

2 2 Liu, Chou, Bgherzdeh digitl ssistnts (PDAs) will likel inlude solr pnels s found in mn lultors tod. Yet nother emple is the distriuted sensors. The re eing uilt tod to drw energ from solr power, wind power, or even oen wves. The represent gret improvement euse the enle the sstem s ontinued opertion for useful or ritil tsks when the trditionl energ soures like tter nd A/C eome unville. These new tpes of energ soures re posing new hllenges to designers of power-wre sstems. Wht the ll hve in ommon is tht mn of these new energ soures re fr from eing idel power supplies. For emple, the output of portle solr pnel tod n e up to 15W under diret sunlight, or down to 1mW under inndesent light. Similrl, other soures will e determined the wind or oen wve, whih n lso use the ville power to vr severl orders of mgnitude. Emedded sstems powered suh soures must e designed to operte in s wide rnge s possile. Indeed, new emerging omponents suh s the Intel XSle re le to sle their power/performne over 2, nd this dnmi rnge will likel to inrese. While low power opertion is lerl importnt, the ilit to full eploit the ville power when energ is undnt is equll importnt. However, tod s sstems let muh free energ go to wste, euse the re designed for fied udgets. For emple, sstem with n XSle drws pproimtel 1W of power, ut when the solr pnel outputs 15W in diret sunlight, up to 14% of the power will e wsted. Even if there is rehrgele tter, when it eomes full hrged, the etr power turns into wste het. This is lso the se with the Mrs rover, whih omplishes its low-power propert serilizing ll tsks, inluding mehnil nd heting s well s omputtion. However, it lso disrds eess power s wste het. One w to tke dvntge of the eess power is to inrese prllelism. In ft, prllelism is in generl n effetive w for oth high performne nd low power. B operting dditionl proessors t their pek rte, the will e le to tke dvntge of the undnt energ. Prllelism n lso enle set of proessors to operte t lower power level thn single proessor with the sme performne. Although it is diffiult to prllelize lgorithms in generl, sstems with mn onurrent tivities present mn opportunities for prllelism-sed trde-offs. Pek-power poses new hllenges to suh power-wre rhiteture with multiple proessors. Tod s sstems stisf the pek-power onstrint onstrution, tht is, eh omponent is given udget tht is gurnteed never to e eeeded ording to their dt sheet. However, using multiple proessors to full utilize the ville power when undnt, multi-proessor rhiteture would risk eeeding the totl udget when the suppl power is low, if it is not designed refull. Therefore, it is of utmost importne tht the proposed sheme e le to full respet the mimum power s hrd onstrint. In this pper, we propose to enhne the dnmi rnge of these emedded sstems mens of tsk motion nd power-wre sheduling. It trnsforms tsks within their timing onstrints nd their preedene dependenies in order

3 Power-Awre Tsk Motion 3 to mth the prllelism to the ville power level. Furthermore, we eploit domin-speifi knowledge out the power-onsuming tsks to hieve dditionl signifint power/performne improvements over eisting shedulers. The enhned dnmi rnge nd power-wreness enle the sstem to omplish more tsks in shorter mount of time while respeting ll timing onstrints. The enefits must ultimtel e trnslted into pplition-speifi metris, ut s power-wre sstems re deploed in more mission-ritil pplitions, the sving from redued mission time or enhned qulit m trnslte into sving of millions of dollrs. Setion 2 reviews relted work. Setion 3 uses n emple showing ounterintuitive result when some of the well-known tehniques will fil t the sstem level. However, this prolem n e suessfull ddressed our new tehnique, whih is presented in Setion 4. We disuss eperimentl results in Setion 5. 2 Relted Work To eplore the power/performne rnge in power-wre emedded sstems, we n drw from mn tehniques developed for low power nd high performne. This setion surves relted work in these res with disussion on their integrtion t the sstem level. Low power n e hieved mn ws. For sstem-level designs, where the omponents re lrgel off-the-shelf or lred designed, the pplile tehniques inlude susstem shutdown nd dnmi voltge sling (DVS). In the first se, susstem shutdown deision n e sed on fied idle times, dptive timeout, or preditive sed on mi of profile nd runtime histor [15, 14, 4]. Similrl, power-up m e either event-driven or preditive in n ttempt to minimize timing or power penlt. In the seond se, DVS tehniques hve een developed for vrile-voltge proessors (introdued [16], with follow-up [5, 12] nd more). Beuse energ is qudrti funtion of voltge, lowering the voltge n result in signifint sving while still enling the proessor to ontinue mking progress, unlike the shutdown se. Lowering the voltge will lso require redution in frequen, whih hs the effet of reduing dnmi swithing power. In ddition to low power, the power/performne rnge n lso e inresed towrds high performne drwing from previous work on retiming or pipelining nd ppling them to the sstem level. Leiserson et l. first estlished the theoretil foundtion for retiming snhronous iruits [8], nd this hs een etended to loop sheduling for VLIW proessors [13, 2, 6]. Shifting tsks in dt flow grph (DFG) ross the itertion oundr n result in shorter eeution time or llevite the resoure pressure (e.g. numer of registers nd funtionl units). Suh tehniques re lso used in power minimiztion reduing swithing tivities [7, 17]. Eisting tehniques need signifint enhnements efore the n e orretl pplied to sstem-level power mngement prolem. First, most tehniques to dte tret either power or timing s n ojetive, rther thn on-

4 4 Liu, Chou, Bgherzdeh strint. In rel sstems, the m power udget is rel, hrd onstrint, whose violtion n led to mlfuntion. M power ws not of entrl onern previousl, ut s we onsider dditionl power soures suh s solr whose power output n vr, m power onstrints must e stritl enfored. This eomes espeill importnt s we inrese the rnge of power nd performne trdeoffs tuning the prllelism. Seond, the tsks to e sheduled re relted to eh other not onl preedene, dt dependen or dedline, ut lso relted ross different omponents dependenies like o-tivtion, whih must e orretl modeled for sstem-level power mngement, or else nomlies n our. Co-tivtion mens the eeution of one tsk requires the power onsumption of other dependent servies or tsks. A simple emple is tht when the CPU is running, it imposes o-tivtion dependen on the memor. Tehniques suh s DVS re designed minl for minimizing CPU power, ut the hve not onsidered other omponents tht hve dependenies on the CPU. In ft, energ sved on the CPU m e more thn offset the inresed energ onsumed the rest of the sstem. The following setion presents simple emple to illustrte suh n noml with ppling DVS without sstem-level onsidertions. 3 DVS Anoml We present simple emple in Fig. 1 to illustrte n noml with ppling DVS without onsidering sstem-level dependenies, resulting in n inorret sstem. It will e further used to eplin our new sstem model nd sheduling tehnique in the ensuing tet. In this emple, five tsks,,,, re to e sheduled on four eeution resoures A, B, X, Y. The onstrints re: 1. The overll dedline is t time The m power udget is 1W. 3. Tsks, nd must e serilized. 4. The eeution resoures A, B re not voltge-slle. 5. Onl tsk n e voltge-sled on resoure X (e.g. proessor), nd it hs some slk time to finish efore time Tsk must o-tivte with tsk, nd its resoure Y is lso not voltgeslle (e.g. memor, I/O). Note tht tsk need not strt nd finish t the sme time s, ut it must envelop, i.e., strt no lter thn strts nd finish no sooner thn finishes. For simpliit, this emple ssumes nd strt nd finish together. We present shedules s power-wre Gntt hrts, where the horizontl nd vertil es represent time nd power, respetivel. Eh hrt lso onsists of pir of views: time view orgnizes tsks horizontl trks tht orrespond to power onsuming resoures (proessors, peripherls), nd power view stks the tsks over time to show the power rekdown tsks. The urve tht tres the height of the power view is the power profile for the entire sstem.

5 Power-Awre Tsk Motion 5 A B X tsk hs dedline 2 Y tsk o-tivtes with tsk Power 12 eeeding m power udget 1 8 Pm: Energ: 19 2 () The shedule is not vlid sine m power udget is eeeded t time slot [,1] due to prllel tsks, nd. A B X Y Power is slowed down to sve power/energ 's eeution del inreses o-tivting with eeeding m power udget Pm: 1 Energ: 21 () DVS tehnique redues power nd energ onsumption of tsk. However, it fils to produe vlid shedule to the entire sstem. The energ omsumption of the whole sstem is inresed o-tivtion. more energ prolog loop od n e iterted fter time 1 A B shift tsks, to previous itertion X [1] from net iter. Y [1] from net iter Time Power Pm: [1] from net iter. Energ: [1] from net iter Time () Our tsk motion tehnique shifts tsk nd its o-tivted tsk to the previous itertion suh tht the m power udget is stisfied. Fig. 1. An emple where DVS fils to redue power nd energ t sstem level, while our new tehnique will sueed

6 6 Liu, Chou, Bgherzdeh Fig. 1() shows time-vlid shedule with m power violtion during time [, 1]. Resheduling nd in [1, 2] will e time-vlid ut still violtes m power. Fig. 1() shows the se when DVS ws used to slow down tsk until its dedline of time 2. Intuitivel, reduing oth power nd energ of tsk should eliminte the m power violtion, ut insted it not onl does not redue m power, ut tull inreses totl energ t the sstem level. Beuse runs more slowl, its o-tivted tsk must lso onsume power for longer on devie tht is not voltge slle. As result, the eeution of nd overlps tht of tsk, there leding to higher sstem-level power. Furthermore, energ sved slowing down is more thn offset the dditionl energ onsumed the lengthened. This noml is n emple where DVS should not e pplied in isoltion. Fig. 1() shows fesile solution otined our new power-wre tsk motion tehnique on itertive tsks. Tsk nd re shifted (or promoted) to the previous itertion to overlp tsk insted of or. As result, oth the m power nd the dedline re stisfied. However, the optiml solution nnot e otined unless we eploit domin-speifi knowledge out the tsk set eliminting preedene dependen nd repling it with utiliztion onstrint. The detils will e eplined in lter setions. 4 Tsk Motion under Timing nd Power Constrints We propose power-wre tsk motion for eploring power/performne trdeoffs in emedded sstems. We first define our onstrint model nd introdue our representtions sed on timing onstrint grph, where we pture two lsses of onstrints: intr-itertion nd inter-itertion timing onstrints. Tsk motion shifts tsks ross itertion oundries nd reles timing onstrints to hieve more sheduling opportunities. We lso define utiliztion onstrints to support more ggressive ut provl orret design spe eplortion. We lose this setion skething n lgorithm tht omines power-wre sheduling [9, 1] nd tsk motion s new kno for power-wre designs. 4.1 Constrint grph nd shedule The input to the sheduler is (timing) onstrint grph G(V, E), where the verties V represent tsks, nd the edges E V V represent timing onstrints etween tsks. Eh verte v V hs three ttriutes, d(v), p(v) nd r(v), representing tsk v s eeution del, power onsumption nd resoure mpping, respetivel. Eh edge (u, v) E hs two ttriutes, δ(u, v) nd λ(u, v). δ(u, v) speifies the min/m timing onstrints [3]. For n funtion σ tht ssigns the strt times to tsks u nd v s σ(u) nd σ(v), σ(v) σ(u) δ(u, v). If δ(u, v), then the edge (u, v) is lled forwrd edge, nd it speifies min timing onstrint. If δ(u, v) <, then it is kwrd edge inditing m timing onstrint. λ(u, v) is lled the dependen depth, whih speifies onstrints ross itertions. An itertion is full pss of eeuting eh tsk

7 Power-Awre Tsk Motion 7 one in vlid order. δ(u, v) nd λ(u, v) indite tht the eeution of tsk u in itertion i must preede tsk v in itertion i + λ(u, v) δ(u, v) time units. If λ(u, v) =, edge (u, v) speifies n intr-itertion onstrint. Otherwise, it is n inter-itertion onstrint. We ssume tht inter-itertion onstrints re onl preedene dependenies (forwrd edges) nd their dependen depths re positive integers. For kwrd edges, their dependen depths re lws zero. A shedule σ ssigns strt time σ(v) to eh tsk v V. It hs finish time τ σ when ll tsks omplete their eeution. Shedule σ is lled time-vlid if ll the strt time ssignments stisf ll timing onstrints, nd tsks tht shre the sme resoure re serilized. If G represents n itertion of loop, σ must lso stisf inter-itertion onstrints suh tht the must hold ross itertions when multiple instnes of σ re ontented. A shedule σ hs power profile funtion of time P σ (t), t τ σ representing the instntneous power onsumption of ll tsks during the eeution of σ (illustrted the power view of the Gntt-hrt in Fig. 1). The power profile is onstrined two prmeters: P m, P min, suh tht P m P σ (t) P min. The m power onstrint P m speifies the mimum level of power tht n e supplied the power soures. The min power onstrint P min speifies the level of power onsumption to mintin preferred level of tivit. The m power onstrint is hrd onstrint. At n given time t, the vlue of the power profile funtion P σ (t) must not eeed P m. Shedule σ is lled power-vlid (or simpl, vlid) if it is time-vlid nd its power profile does not eeed the m power onstrint. However, we tret the min power onstrint s soft onstrint tht ould e violted osionll in vlid shedule. In ses where the min power onstrint P min represents the free power level (e.g. solr), the energ drwn from the non-renewle energ soures is defined s the energ ost E σ (P min ) of shedule σ. It distinguishes etween ostl power nd free power in suh w tht n power onsumption elow the free power level does not ontriute to the energ ost on non-renewle energ soures, nd therefore should e utilized mimll. 4.2 Tsk motion under timing onstrints Tsk motion otins different versions of sheduling prolem onverting etween intr-itertion nd inter-itertion onstrints. We first onstrut n itertion grph G (V, E ): it hs the sme verties s those of the onstrint grph G(V, E), ut edges E onsist of onl intr-itertion onstrints. Formll, E = {(u, v) : (u, v) E suh tht λ(u, v) =, δ (u, v) = δ(u, v)}. The edges in E will not hve dependen depths λ, sine the re lws zero. The epeted loop durtion τ is otined from the originl shedule omputed from the initil itertion grph G. Without loss of generlit, we fous our disussion on tsk promotion whih the eeution of tsk is shifted to the previous itertion of the loop, nd the instne of the sme tsk in the net itertion is promoted into the new loop od. The inverse proedure for tsk demotion n e similrl defined.

8 8 Liu, Chou, Bgherzdeh A tsk v is promotle if either verte v V does not hve n inoming forwrd edges, or ll of v s inoming forwrd edges in G hve t lest one dependen depth. If σ is vlid shedule of one itertion, we n promote tsk v ording to the epeted loop durtion, whih is the finish time τ σ of σ. Given τ = τ σ, promoting tsk v entils the following trnsformtions on G nd G : 1. For eh of v s inoming forwrd edges (u, v) in grph G, derese λ(u, v) one. If (u, v) eomes n intr-itertion onstrint, (λ(u, v) = ), edge (u, v) is dded to grph G if it is not present in G. 2. For eh v s outgoing forwrd edge (v, u) in grph G, inrese λ(v, u) one. 3. For eh v s inoming kwrd edge (u, v) in grph G, inrese δ (u, v) τ, tht is, δ (u, v) = δ (u, v) + τ. 4. For eh v s outgoing edge (v, u) in grph G, derese δ (v, u) τ, tht is, δ (v, u) = δ (v, u) τ. Steps 1 nd 2 push one dependen depth from v s inoming forwrd edges to its outgoing forwrd edges. Step 1 lso dds n new intr-itertion edges to grph G, whih trks onl intr-itertion onstrints. Step 3 trnsforms the inoming kwrd edges of v for the promotion (its inoming forwrd edges re mnged in step 1). Step 4 trnsforms the outgoing edges of v, for oth forwrd nd kwrd edges. Steps 3 nd 4 n e vlidted s follows. When tsk v is promoted in grph G, verte v represents the eeution of tsk v in the net itertion. Therefore, the new strt time ssignment σ (v) = σ(v)+τ. In step 3, efore promoting v, edge (u, v) indites σ(v) σ(u) δ (u, v). Thus fter the promotion, σ (v) σ(u) = (σ(v) + τ) σ(u) δ (u, v) + τ. Therefore, the new onstrint in G is δ (u, v) + τ. Similrl in step 4, edge (v, u) mens σ(u) σ(v) δ (v, u) efore promotion. Thus, σ(u) σ (v) = σ(u) (σ(v) + τ) δ (u, v) τ. The onstrint eomes δ (u, v) τ fter the promotion. When tsk v is eing promoted, its orresponding min timing onstrints (zero or positive vlues) will eome m timing onstrints (negtive vlues) step 4; nd vie vers, its orresponding m timing onstrints will trnsform into new min timing onstrints step 3. Promotion effetivel redues the vlues of min onstrints nd mkes the prolem esier to solve eposing more sheduling opportunities. We s tht the onstrint is reled, nd this is ke tehnique for inresing the sstem s dnmi rnge. Fig. 2 illustrtes tsk promotion on the emple previousl shown in Fig. 1. Fig. 2() shows the initil onstrint grph G onsisting of five verties representing five tsks,,,,. The ll hve the sme eeution del of one time unit, nd their power onsumption is p() = 3W, p() = 6W, p() = 2W, p() = p() = 4W. Therefore the most power onsuming tsk is nd the lest power onsuming one is. Tsks,, hve dedited eeution resoure A, X, Y (r() = A, r() = X, r() = Y ), respetivel; while tsks nd shre the eeution resoure B (r() = r() = B). For revit, these tsk ttriutes re not shown in the grph. The edges in the onstrint grph G represent timing onstrints. The re denoted s (λ, δ) orresponding to the dependen depths nd the vlues of the timing onstrints.

9 Power-Awre Tsk Motion 9 For emple, the forwrd edge (, ) represents n intr-itertion onstrint with dependen depth λ(, ) =, nd it is min onstrint with δ(, ) = 1 inditing σ() σ() 1. Sine tsk s del d() = 1, this onstrint n e prphrsed s tsk nnot strt until tsk ompletes, tht is, tsks nd must e serilized. Similrl tsks nd re lso serilized edge (, ). Edge (, ) with δ(, ) = indites tht tsk nnot strt efore tsk strts, euse σ() σ(). Edge (, ) with δ(, ) = 2 speifies min seprtion etween tsk nd tsk, tht is, σ() σ() 2. Therefore, tsk must wit until tsk hs strted for two time units. Edge (, ) with δ(, ) = 2 is kwrd edge representing m onstrint: σ() σ() 2. It defines the dedline to strt tsk reltive to the strt time of tsk. This dedline is equl to the strt time of tsk plus two time units. In ddition to these intr-itertion timing onstrints, there is n inter-itertion timing onstrint (, ), inditing tht the strt time of tsk preedes tsk in the net itertion (λ(, ) = 1) one time unit (δ(, ) = 1). Inter-itertion onstrints re mrked s dshed rrows. There is o-tivtion dependen etween tsk nd tsk. This is denoted s pir of speil timing onstrints. As mentioned previousl, we ssume eh itertion must finish within three time units. The initil itertion grph G hs the sme set of verties representing tsks,,,,. The edges in G onl represent intr-itertion onstrints. Therefore onl the onstrint vlue δ is shown on eh edge. Dependen depth λ is not shown sine it is lws zero in grph G. For emple, the inter-itertion edge (, ) does not pper in the initil G. The o-tivtion dependen is still denoted s speil onstrint in G. The initil shedule σ omputed from the itertion grph G is lso shown in Fig. 2(). It is the sme s Fig. 1(). Although ll timing onstrints re stisfied, the shedule σ is not vlid sine during time [, 1] the power onsumption of the whole sstem is 11W, eeeding the m power onstrint P m = 1W. No vlid solution is possile even if we tr voltge sling for tsks. In Fig. 2() tsk nd its o-tivted tsk re promoted to produe vlid shedule (sme s Fig. 1(), eept tht the prolog is not shown). Tsks nd re promoted together due to o-tivtion, ut the re sheduled s seprte tsks euse the m not strt nd finish t the sme time. The onstrint grph G will onl updte dependen depths λ of the timing onstrints orresponding to. Sine the originl shedule finishes t time 3, the timing onstrints δ in G will e trnsformed using τ = 3. B step 1, edge (, ) G eomes n intr-itertion edge (solid rrow) nd is inserted to G. B step 2, edges (, ) nd (, ) G eome inter-itertion edges (dshed rrows). B step 4, edges (, ) nd (, ) G redue their onstrint vlues τ = 3. Aordingl, tsk s outgoing min onstrints re trnsformed into more reled m onstrints (δ (, ) = 3, δ (, ) = 1, ompred to nd 2 in Fig 2()). As result, tsks n e resheduled in time slot [2, 3] without violting n timing onstrints, nd the m power onstrint is lso stisfied. Without tsk motion, this vlid solution nnot e hieved.

10 1 Liu, Chou, Bgherzdeh 4.3 Utiliztion onstrints Tsk motion is sed on the lssifition of intr-itertion nd inter-itertion timing onstrints. However, in some ses, it is diffiult or unneessr to deide whether timing onstrint should e intr-itertion or inter-itertion. Suh ses re present in the Mrs rover. For emple, for timing onstrints etween heter nd motor whih the motor is heted periodill, whether to model these onstrints s intr-itertion or inter-itertion is not ler. In ft, whether the heters nd the motors st in the sme itertion does not mtter. In the omputtion domin, these orrespond to kground, preemptile tsks tht need not snhronize with the min ontrol loop ut must e given shre of the CPU time to void strvtion. Constrint grph G Itertion grph G' Shedule σ A B (,) (,1) 1 X (1,1) -2 Y (, -2) (,2) (,1) 2 1 Power o-tive o-tive () efore tsk motion, no vlid solution n e found. o-tive (1,) (,1) (, -2) (1,2) (,1) o-tive (,1) () fter promoting tsk nd o-tivting tsk, vlid solution is found. o-tive (*,) (,1) (*, -2) (1,2) (,1) o-tive (*,1) () fter promoting tsk with utiliztion onstrints, new solution with etter performne is found. -2 A B X Y -2 Power A B X Y -2 Power [*] [*] Energ: 19 Pm: 1 [1] [1] Pm: 1 [1] [1] Energ:19 [1] [1] 1 2 Time Pm: 1 [1] Energ: 19 [1] 1 2 Time Fig. 2. Tsk motion under timing onstrints We ll suh onstrints utiliztion-sed timing onstrints. The n e epressed s either intr-itertion or inter-itertion ones. A utiliztion onstrint etween two tsks u nd v is lso represented s n edge (u, v) E in onstrint grph G with its dependen depth denoted s λ(u, v) =, inditing tht it n e either zero or non-zero.

11 Power-Awre Tsk Motion 11 Now we emine tsk motion under utiliztion onstrints. It needs onl minor modifitions to the proedure we defined in Setion 4.2. () The initil itertion grph G will inlude oth intr-itertion onstrints nd utiliztion onstrints in its edges. (Tret utiliztion onstrints s intritertion). () A tsk v is promotle if either verte v V does not hve n inoming forwrd edges, or the dependen depths λ of ll v s inoming forwrd edges re positive vlues or. (Tret utiliztion onstrints s inter-itertion). () The modified proedure for promoting tsk v is s follows. 1. For eh of v s inoming forwrd edges (u, v) in grph G, derese λ(u, v) one, if λ(u, v). If λ(u, v) eomes, dd edge (u, v) to grph G if it is not present in G. (No updte for utiliztion onstrints in step 1). 2. For eh v s outgoing forwrd edge (v, u) in grph G, inrese λ(v, u) one, if λ(u, v). (No updte for utiliztion onstrints in step 2). 3. For eh v s inoming kwrd edge (u, v) in grph G, δ (u, v) = δ (u, v) + τ, if λ(u, v). Otherwise, δ (u, v) remins unhnged. (No updte for utiliztion onstrints in step 3). 4. For eh v s outgoing edge (v, u) in grph G, δ (v, u) = δ (v, u) τ. (Sme s the previous step 4). Sine utiliztion onstrints n e either intr-itertion or inter-itertion, giving them some speil tretments, the modified proedure is strightforwrd eept steps 3 nd 4 need more eplntion. In step 3, if edge (u, v) represents utiliztion onstrint, δ (u, v) n e trnsformed into either one of the two forms: δ (u, v) or δ (u, v) + τ, sine it n e either intr-itertion or interitertion. Tht is, the trnsformtion is vlid either σ (v) σ(u) δ (u, v) or σ (v) σ(u) δ (u, v)+τ holds. Oviousl, the solution to these two inequlities with n OR reltion is σ (v) σ(u) δ (u, v), whih mens the onstrint with the smller vlue pplies. Therefore, the vlue of utiliztion onstrint will not inrese τ in step 3. Likewise, in step 4, the vlue of the new onstrint is the smller one etween δ (v, u) τ nd δ (v, u), whih is δ (v, u) τ. In summr, if the promoted tsk v hs n inoming utiliztion-onstrint edges, then these edges remin the sme in the itertion grph G during the promotion. For v s outgoing utiliztion-onstrint edges, the vlues of onstrints in G re deresed the loop durtion τ. As result, utiliztion onstrints will lws e reled to produe more sheduling opportunities. For emple, if resoure A is heter, motor, or CPU running preemptile kground tsks, then we n model tsk with utiliztion onstrints (, ), (, ) nd (, ). The initil grphs G, G nd shedule σ look ver similr to Fig. 2(), eept utiliztion onstrints (, ), (, ) nd (, ) in G will e denoted s new tpe of rrows, nd their dependen depths λ = (s seen in Fig. 2()). After promoting tsks nd, grphs G, G nd shedule σ will lso look similr to Fig. 2() eept tht the utiliztion onstrints (, ), (, ) nd (, ) in G will not e hnged tsk motion.

12 12 Liu, Chou, Bgherzdeh Fig. 2() shows the resulting grphs G, G nd shedule σ fter promoting tsk with utiliztion onstrints, whih re mrked s different tpe of dshed rrows in grph G. B the modified step 3, the vlue of onstrint δ (, ) in G will remin 2; otherwise it will e resumed to 1 if it is not utiliztion onstrint. The sme rule lso pplies to utiliztion onstrint (, ) suh tht δ (, ) = 3 insted of. Sine the seriliztion hin formed min onstrints is roken, tsks,, (fter promoting, the hin eomes,, in Fig. 2()) no longer need to e serilized. Now tsk, smll power onsumer, n overlp suh tht n unepeted solution with shorter eeution time (τ σ = 2) is disovered, nd it lso stisfies the m power onstrint. This optiml solution ould not hve een otined without using utiliztion onstrints, whih enle more ggressive, provl orret reltion of the time onstrints. 4.4 Sheduling lgorithms for power-wre tsk motion We omine power-wre sheduling with sstem-level tsk motion s w to disover wider rnge of power/performne trde-offs. Our ore sheduling lgorithms onsist of () trnsforming the prolem into its new versions tsk motion, nd () power-wre sheduling for eh version. From the illustrtion in Setions 4.2 nd 4.3, the implementtion of () is strightforwrd. Algorithm () is derived from [1] ppling the power-wre sheduler to the itertion grph G fter eh tsk motion. For revit, detils of the sheduling lgorithms re omitted in this pper ut n e found in [11]. 5 Eperimentl Results We use the NASA/JPL Mrs rover [1] to evlute the effetiveness our powerwre tsk motion tehnique. We onstrut sstem-level representtion tht inludes the omputtionl, mehnil nd therml susstems. The timing onstrints on the heters nd preemptile kground omputtion tsks n e modeled with utiliztion onstrints. We lso onsider dul energ soures: solr pnel nd non-rehrgele tter. We onsider three senrios with different solr power output levels: 14.9W (noon time), 12W, nd 9W (dusk). The min power onstrints re set to the respetive solr output levels, while the m power onstrints re set to the solr power plus 1W, whih is the mimum tter power rting. Tle 1 ompres the results of four tehniques using the energ ost to the non-rehrgele tter nd the eeution time of eh itertion s metris: () the eisting mnul solution (full serilized), (I) power-wre sheduling [1], (II) power-wre tsk motion without utiliztion onstrints, (III) power-wre tsk motion with utiliztion onstrints. For senrio 1 (14.9W solr power), ll shedulers eept JPL s () ompute fst shedules (i.e., short τ), ut these three solutions vr in energ ost.

13 Power-Awre Tsk Motion 13 Solutions shedulers I nd II re eliminted, euse the must drw more energ from the tter in ddition to the solr pnel in order to hieve the sme performne s solution III. Sheduler III ould not hve hieved this solution without eploiting utiliztion onstrints. For senrio 2 (12W solr power), shedulers I nd II produe the sme solution tht is slower thn in senrio 1 due to the limited power udget. Sheduler III produes fst shedule t higher energ ost thn I nd II, ut it is still within the m power onstrint. No one solution is stritl etter thn the other, nd the represent different trde-off points. In senrio 3 (9W solr power), the low power udget rules out ll ut the full serilized solution, nd ll shedulers produe the sme solution s JPL s mnul shedule (). Senrio () JPL's Low-power (hnd-rft) (I) Power-wre (II) Power-wre + Tsk motion (III) Power-wre + Tsk motion + Utiliztion onstrint τ = 75s E = J τ = 5s E = 79.5J τ = 5s E = 16.5J τ = 5s E = 4.5J τ = 75s E = 55J τ = 6s E = 147J sme s (I) τ = 5s E = 28J τ = 75s E = 388J sme s () sme s () sme s () = keep = drop Tle 1. Comprison in three senrios JPL Tsk motion A Tsk Motion B Time (--) (III-I-) (III-III-) Senrio frme (s) Distne Time Energ Distne Time Energ Distne Time Energ (step) (s) ost (J) (step) (s) ost (J) (step) (s) ost (J) Totl Improvement 33% 33% 49% 24% Tle 2. Comprison in omprehensive senrio The results show tht our tehnique not onl ields lrger dnmi rnge eing le to operte t different power levels, ut more importntl it uses the ville energ more effetivel for tul useful work. This is not es due to omple timing onstrints, ut the improvement n trnslte into signifint svings in pplition-speifi metris, s shown in Tle 2. Suppose the rover is trveling to trget lotion in distne of 48 steps. Sine the rover moves two steps during eh itertion, it needs 24 itertions to

14 14 Liu, Chou, Bgherzdeh reh the destintion. The mission strts with mimum solr power t 14.9W (Senrio 1). Then, it drops to 12W (Senrio 2) fter 1 minutes, nd flls to 9W (Senrio 3) 1 minutes lter. If the eisting low-power, seril shedule is pplied, the rover will spend 1 minutes evenl in ll three senrios t fied slow moving speed. This results in long eeution time nd high energ ost in Senrio 3. On the other hnd, our tehnique n produe two shemes. Both shemes use more free solr energ to speed up in senrios 1 nd 2 (while stisfing timing nd power onstrints) so tht the n finish the mission erlier to void the ostl senrio 3. Shemes A nd B differ onl in senrio 2 where A uses solution I while B uses the fster ut more epensive solution III. As result, sheme A hieves 33% speedup nd 33% energ sving; nd sheme B further speeds up 49% with 24% energ redution. These two lterntive designs with different energ/performne trde-offs re disovered our power-wre tsk motion tehnique. The ould not hve een found the eisting tehniques. 6 Conlusion We hve presented power-wre tsk motion tehnique for enhning the dnmi rnge of emedded sstems powered heterogeneous energ soures tht inlude renewle, unsted ones like solr pnels. The must e le to not onl operte s low-power devies when the suppl power is low, ut equll importntl use the free undnt energ for useful work while respeting power nd timing onstrints. We used DVS Anoml emple to show the pitflls of ppling eisting power mngement tehniques without onsidering sstem-level dependenies like o-tivtion, nd this hs resulted in not onl higher energ onsumption ut lso violtion of m power onstrints. We then showed our onstrint formultion nd tsk motion tehnique to sfel trnsform the tsks while respeting these sstem-level dependenies. We further enhned tsk motion eploiting utiliztion-sed onstrints tht eposed dditionl sheduling opportunities for preemptile, kground tsks or even non-omputtionl power onsumers suh s heters. These ll served to enhne the dnmi rnge while ensuring ll trnsformtions re sfe nd provl orret. Eperimentl results on the Mrs rover demonstrted the effetiveness of our pproh for the solr- nd tter-powered sstem. We epet the enefits to trnsfer to whole emerging lss of new emedded sstems tht must drw energ from mn renewle ut unsted soures. Aknowledgement This reserh ws sponsored DARPA grnt F nd Printroni Fellowship. It represents ollortion etween the Universit of Cliforni t Irvine nd the NASA/Cl Teh Jet Propulsion Lortor. Speil thnks to Dr. N. Arnki, Dr. B. Toomrin, Dr. M. Mojrrdi nd Dr. J. U. Ptel t JPL nd Kerr Hill t AFRL for their disussion nd ssistne.

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