Partitioned EDF Scheduling in Multicore systems with Quality of Service constraints

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1 Parttoned EDF Schedulng n Multcore systems wth Qualty of Servce constrants Nadne Abdallah, Audrey Queudet, Marylne Chetto, Rafc Hage Chehade To cte ths verson: Nadne Abdallah, Audrey Queudet, Marylne Chetto, Rafc Hage Chehade. Parttoned EDF Schedulng n Multcore systems wth Qualty of Servce constrants. 18th IEEE Internatonal Conference onelectroncs, Crcuts and Systems (ICECS), 2011, Dec 2011, berut, ebanon. pp , 2012, < /ICECS >. <hal > HA Id: hal Submtted on 27 Feb 2013 HA s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. archve ouverte plurdscplnare HA, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 Parttoned EDF Schedulng n Multcore systems wth Qualty of Servce constrants Nadne Abdallah, Audrey Queudet, Marylne Chetto, Rafc Hage Chehade IRCCyN Unversty of Nantes, Nantes, France Emal: frstname.lastname@rccyn.ec-nantes.fr INA Unversty of Nantes, Nantes, France Emal: audrey.queudet@unv-nantes.fr IUT Sada ebanese Unversty, Sada, ebanon Emal: rhagechehade@ul.edu.lb Abstract In ths paper we study the parttoned EDF schedulng n a homogeneous multprocessor envronment wth Qualty of Servce (QoS) constrants. The system consdered here s a real-tme multprocessor system assumed to be powered by rechargeable batteres. We address the ssue of how to best partton a set of frm real-tme tasks that can occasonally skp one nstance accordng to a predefned QoS threshold. The man goal s to mnmze the energy consumpton of the system whle offerng solutons wth respect to transent energy starvaton stuatons the system can experment. The contrbuton of the paper s twofold. Frst, we present a schedulablty analyss of frm multprocessor task sets under QoS constrants. Second we propose new parttonnng heurstcs ntegratng skps. The evaluaton s conducted from several ponts of vew (mnmzaton of the total processor number, maxmzaton of the spare capacty on each processor). I. INTRODUCTION The computer scence lterature generally dvdes real-tme systems n three man categores: soft, hard and frm [10]. Soft real-tme systems allow some jobs to mss ther deadlnes n order to mprove resource usage or average performance. Hard real-tme systems embody guaranteed tmng and cannot mss deadlnes. A sngle falure n one tmng constrant can cause an ntolerable cost (n terms of human lves, equpment damage or economc loss). Frm real-tme systems nstead allow some of ther constrants to be occasonally lost, the performance beng then quantfed n terms of Qualty of Servce (QoS). In recent years, there has been ncreasng nterest to ncorporate real-tme schedulng technques that deal wth power/energy conservaton. Many energy-orented real-tme schedulng technques have been proposed to reduce energy consumpton. Among them, Dynamc Voltage and Frequency Scalng (DVFS) algorthms [5] reduce energy consumpton by changng processor speed and voltage at run-tme dependng on the needs of the applcatons runnng. Another trend s based upon Dynamc Power Management (DPM) polces [3] whch trade off the performance for the power consumpton by selectvely placng components nto low-power states. All these technques have been proposed for unprocessor realtme systems. However, wth todays computatonal demands and as the mnaturzaton of ntegrated crcuts reaches ts physcal lmts, a vald soluton to supply suffcent resources s to use multcore platforms, but actually, much less work has been done for power awareness n multcore systems. In our research we consder multcore real-tme systems wth both QoS and energy constrants. The objectve s to explot the flexblty offered by QoS-based real-tme tasks to face both processor overload and energy starvaton stuatons, skppng the executon of some task nstances. For that purpose, we propose to tackle the problem of the repartton of QoS-constraned tasks over such platforms. Our contrbuton s twofold. Frst, we desgn a schedulablty test for frm multprocessor task sets under QoS constrants. Second, based on ths test, we propose new parttoned schedulng heurstcs to assgn tasks wth QoS constrants to processors, so as to mnmze the number of processors, thus mnmzng the energy consumpton. To the best of our knowledge, ths paper s the frst to ntroduced QoS contrants nto parttonng heurstcs. We rely on prevous parttonng results [12][9][13] to preselect whch parttonng heurstc and whch task set sortng crteron can best ft both QoS and energy constrants. The performance of each heurstc s analyzed accordng to the success rato (.e. the number of schedulable task sets among the total number of generated task sets). We also study the nfluence of the task sortng crtera on the schedulablty of each heurstc so as to underlne the mpact of task sortng crteron on the performance of the heurstcs chosen. The remander of ths paper s organzed as follows: n Secton 2, we descrbe some background materal. Secton 3 presents the models and defntons consdered n ths paper. Secton 4, 5 and 6 presents the man contrbuton whch begns wth a schedulablty analyss under QoS constrants and then reles on the parttonng under QoS contrants to end wth performance evaluaton. In Secton 7, we conclude and gve some future lnes of nvestgaton.

3 A. EDF Schedulng II. BACKGROUND MATERIA Earlest Deadlne Frst (EDF) schedulng algorthm [6] s an algorthm n whch jobs wth earlest deadlnes have hgher prorty. EDF s an optmal schedulng algorthm on preemptve unprocessors, n the followng sense: f a collecton of ndependent jobs can be scheduled (by any algorthm) such that all the jobs complete by ther deadlnes, EDF wll schedule ths collecton of jobs such that they all complete by ther deadlnes. B. Skp-Over model We consder a unprocessor system consstng of frm perodc and preemptable tasks. Tasks are assumed to be ndependent. Each task s dvded nto nstances where each nstance occurs durng a sngle perod of the task. The possblty of skppng task nstances was ntroduced by Koren and Shasha [8]. In ther model, a task s characterzed by ts worst case executon tme, ts perod, ts deadlne and a skp parameter s (2 s ). Ths parameter gves the tolerance of a task to mss deadlnes. The hgher s s, better s the QoS. It represents the mnmum QoS requred by a task. Every nstance of the task can be red or blue. Red nstances must complete before ther deadlne but blue nstances can be skpped or aborted at any tme. A task set s deeply-red when all tasks nstances are ntally actvated at the same tme and are red. The dstance between two consecutve skps must be at least s perods. After mssng a deadlne, the next s 1 nstances must complete before ther deadlnes. On the contrary, f a blue nstance completes wthn ts deadlne, the next nstance s stll blue. Here are two algorthms based on the Skp-Over model: RTO (Red Tasks Only): ths algorthm never tres to execute blue nstances. Red nstances only are scheduled accordng to EDF. In the deeply-red model, ths algorthm s optmal whch means that all feasble task sets wll be schedulable usng RTO. BWP (Blue When Possble): ths algorthm s more flexble n the sense that t schedules red nstances accordng to EDF and tres to schedule blue nstances when there are no ready red nstances. C. Parttonng Parttonng a task set s equvalent to the Bn-Packng problem: how to place n objects of dfferent szes n m dentcal boxes. Ths problem s known to be NP-hard. The only known soluton for ths knd of problem s to enumerate all possble confguratons and verfy ther correctness one by one. Some heurstcs [12][9][13] have been proposed n the lterature n order to solve t. All of them mply a sequental assgnment of tasks to processors: a task s assgned on a processor f t verfes the schedulablty test after assgnment. Accordng to Frst Ft (FF) a task s assgned to the frst possble processor, startng from π 1 (the frst processor). Best Ft (BF) assgns a task τ to the processor whch mnmzes the remanng processor capacty. Accordng to Worst Ft (WF) a task s assgned to the processor whch maxmzes the remanng processor capacty. Next Ft (NF) assgns a task τ to the frst possble processor n the range π j,..., π m (π j beng the current processor). The procedure starts from π 1. A. System and task model III. MODES AND DEFINITIONS In ths paper, we consder π a platform wth m dentcal processors: π = {π 1,..., π m }. We refer to the Skp-Over perodc task model. A perodc task τ s defned by a 4-tuple (C,, D, s ) where C s the worst-case executon tme (WCET), the perod, D the relatve deadlne and s the skp parameter. A task can be nstantated an nfnte number of tmes. The task set τ = {τ 1,..., τ n } s composed of n perodc tasks wth constraned deadlne (D ). Tasks are assumed to be ndependent and preemptable. The system s consdered deeply-red. Each task s characterzed by: an utlzaton factor: u = C an equvalent utlzaton factor ntegratng skps: s 1 s u = C C a densty: δ = mn{d,t }. an equvalent densty ntegratng skps: δ = B. Known results C mn{d,} s 1 s 1) Processor utlzaton factor: Gven a set τ = {τ (, D, C )} of n perodc tasks scheduled on a processor, the processor utlzaton factor s defned as [11]: U τ = =1 C (1) 2) Equvalent processor utlzaton factor: Gven a set τ = {τ (, D, C, s )} of n perodc tasks wth mplct deadlne that allow skps, the equvalent processor utlzaton factor ntegratng skps s defned as [8]: U τ = max 0 { where D(, [0, ]) = s. D(, [0, ]) } (2) 3) oad factor: Gven a set τ = {τ (, D, C )} of n perodc tasks wth arbtrary deadlnes, the load factor s defned as [7]: oad(τ) = max{u τ, sup [Dmn,P ) =1 DBF (τ, ) } (3) where D mn = mn{d 1,..., D n } and P = lcm{p 1,..., P n }. For a gven t, the Demand Bound Functon (DBF) represents the upper bound of the workload generated by all tasks wth actvaton tmes and absolute deadlnes n the same nterval [0, t]: ( DBF (τ, [0, ]) = 1 + D ) C (4)

4 DBF wll be computed for correspondng to absolute task deadlnes between 0 and D mn. 4) Exact schedulablty test: A necessary and suffcent (.e. exact) schedulablty test for EDF for arbtrary deadlnes on unprocessor systems s gven by [11]: oad(τ) 1 (5) IV. SCHEDUABIITY ANAYSIS UNDER QOS CONSTRAINTS 5) New equvalent load factor: Gven a set τ = {τ (, D, C, s )} of n perodc tasks wth arbtrary deadlnes that allow skps, we defne the equvalent load factor as: oad QoS (τ) = max{uτ DBF QoS (τ, ), sup [Dmn,P ) } (6) where D mn = mn{d 1,..., D n } and P = lcm{s 1 P 1,..., s n P n }. Accordng to the RTO algorthm, the DBF changes. Its new equaton s : ( DBF QoS (τ, [0, ]) = 1 + D =1 1 ( 1 + D ) ) (7) C s As the DBF QoS changes ts value only at nstants correspondng to absolute deadlnes, DBF QoS wll be computed for correspondng to absolute tasks deadlnes between 0 and D mn. The equvalent processor utlzaton factor Uτ ntegratng skps s defned as t prevously appears n equaton (2). 6) New exact schedulablty test: A necessary and suffcent (.e., exact) schedulablty test for EDF for arbtrary deadlnes QoS-constraned tasks on unprocessor systems s gven by : oad QoS (τ) 1 (8) V. PARTITIONING UNDER QOS CONSTRAINTS A. Identfcaton of sutable heurstcs As mentoned prevously, parttonng, whch reduces to a bn-packng problem, s known to be NP-Hard. Accordng to prevous results n [12], we wll use two heurstcs : Frst Ft (FF) because t mnmzes the number of processors used (n our case, t wll mnmze the energy consumpton); Worst Ft (WF) because t maxmzes the remanng processor capacty, thus offerng more flexblty for rechargng the system n case of energy starvaton. These heurstcs have been adapted n our case. We systematcally apply a schedulablty test (see equaton (8)) before assgnng a task to a processor. If the test s not verfed we contnue testng on others processors untl we fnd the good one able to accept the task. If a task s not assgned to any processor, t means that the task set s not schedulable. B. New task sortng crtera All the parttonng algorthms proposed n the lterature often nclude task sortng crtera wth the purpose of ncreasng ther success rato (.e. rato of schedulable task sets). A task sortng crtera conssts n orderng the tasks before assgnng them to a processor. It has an nfluence on the tasks assgnment on processors. For nstance, sortng tasks n order of decreasng densty wll force to frst assgn heavest tasks on the processors. Based on the observaton of prevous results n the lterature [12], we retaned three crtera: the densty, the utlzaton factor and the perod. We adapted them to QoS constrants, analyzng the general nfluence of the 4 followng crtera n ncreasng/decreasng order: equvalent densty δ, equvalent utlzaton factor u, perod multpled by skp parameter s and the skp parameter tself s VI. PERFORMANCE EVAUATION In ths secton, we evaluate the performance of all possble combnatons between a seres of 2 parttonng heurstcs (adapted FF and WF) and 8 task sortng crtera (δ, u, s, s consdered n ncreasng/decreasng order). A. Task generaton methodology In our task generaton methodology we consder tasks wth constraned deadlnes (D T ) whch s the hardest assumpton to take. s unformly chosen from [20, 40]; C s set to provde a task utlzaton factor equal to the one gven n nput; D s unformly chosen between C and ; s s unformly chosen from [s mn, s max ] where s mn and s max are nput parameters; m s the number of processors used and s gven as a parameter. We consder m-dentcal processor platforms. For m processors, we generate a system that contans 2 m tasks. [1, n], δ 1, whch means that task densty doesn t exceed the utlzaton capacty of a processor. For our smulatons, we generated 1000 dfferent task sets. B. Performance crtera We evaluate each combnaton of the prevously mentoned parameters accordng to a performance parameter named Success Rato whch s defned by: Success rato = N success N generated (9) where N success denotes the number of task sets successfully scheduled and N generated the total number of task sets generated. Ths crtera helps us to determne whch combnaton schedules the largest number of task sets.

5 C. Expermental results In ths secton, we present an ntal emprcal nvestgaton for QoS-constraned tasks defned accordng to the Skp-Over model, examnng the effectveness of our heurstcs on 4 processors. Ths secton deals wth the mpact of a task sortng crteron on the success rato of schedulablty tests. In the correspondng graphs, D means decreasng, I means ncreasng and E means equvalent. Fg. 1. EDF-based sortng crtera wth WF heurstc VII. CONCUSION Whle low-power unprocessor real-tme systems have fueled much recent work on energy-aware schedulng, the same ssue upon multcore platforms has been somewhat neglected. Motvated by ths, we proposed a flexble soluton based on QoS-constraned real-tme tasks, allowng to skp some task nstances n case of ether processor overload or energy starvaton. The major contrbutons of our study are as follows: () we provde a schedulablty test for multprocessor task sets under QoS contrants, () we propose and evaluate two new parttonnng heurstcs (Frst Fst varant that mnmzes the energy consumpton, and Worst Fst varant that leaves maxmum spare capacty on processors n order to allow the battery to charge). From the smulatons, we showed that the best task sortng crteron are equvalent decreasng densty and equvalent decreasng utlzaton. In the future, we want to extend ths study to sem-parttonng algorthms, provdng a complete analyss wth new evaluaton crtera such as the number of mgratons and preemptons. ACKNOWEDGMENT The work presented n ths paper s sponsored by a CE- DRE project, namely GreenEmbedded, whch s a blateral collaboraton between Unversty of Nantes and the ebanese Unversty. REFERENCES Fg. 2. EDF-based sortng crtera wth FF heurstc wth s n [2, 10] The smulaton results depcted n Fgure 1 and 2 show that, takng all heurstcs together, the sortng crtera whch maxmze the success rato are: Decreasng Equvalent Utlzaton and Decreasng Equvalent Densty. Fgure 1 shows that for task sets wth a total utlzaton factor less than 25% of the platform capacty, all sortng crtera gve the same performance. However, for task sets wth total densty greater than 25% of the platform capacty, Decreasng Equvalent Utlzaton factor and Decreasng Equvalent Densty exhbt the best behavor. Decreasng Equvalent Utlzaton factor s slghtly more effcent than Decreasng Equvalent Densty. Fgure 2 shows that for task sets wth the total utlzaton factor less than 75% of the platform capacty, all sortng crtera gve the same performance. However, for task sets wth total densty greater than 75% of the platform capacty, Decreasng Equvalent Utlzaton factor and Decreasng Densty exhbt the best behavor. In fact, for a total utlzaton factor equals to 3.2, at most 99% of task sets are schedulable wth Frst Ft Decreasng Equvalent Utlzaton and 84% wth Worst Ft Decreasng Equvalent Utlzaton and Densty. In Fgure 1, we also notce for Decreasng Equvalent Utlzaton that when skps are comprsed n [2, 4] we have a better success rato than when skps are comprsed n [2, 10]. In fact, the skp parameter has also an nfluence on schedulablty: the more we authorze skps hgher s the success rato. [1] S. Baruah and N. Fsher, The parttoned multprocessor schedulng of deadlne-constraned sporadc task systems, IEEE Transactons on Computers, Vol.55, No.7, pp , [2] S. Baruah, R. Howell, and. Roser, Algorthms and complexty concernng the preemptve schedulng of perodc real-tme tasks on one processor, Journal of Real-Tme Systems, Vol. 2, pp , [3]. Benn, A. Boglolo, and G. De Mchel, A Survey of Desgn Technques for System-evel Dynamc Power Management, IEEE Trans. VSI Systems, Vol. 8, No.3, pp , 2000 [4] M. Caccamo, G. C. 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