Resource Reservation for Mixed Criticality Systems

Transcription

1 Resource Reservaton for Mxed Crtcalty Systems Guseppe Lpar 1, Gorgo C. Buttazzo 2 1 LSV, ENS - Cachan, France 2 Scuola Superore Sant Anna, Italy Abstract. Ths paper presents a reservaton-based approach to schedule mxed crtcalty systems n a way that guarantees the schedulablty of hgh-crtcalty tasks ndependently of the behavour of low-crtcalty tasks. Two key deas are presented: frst, to reduce the system uncertanty and advance the tme at whch a hgh-crtcalty task reveals ts actual executon tme, the ntal porton of ts code s handled by a dedcated server wth a bandwdth reserved for the worst-case, but wth a shorter deadlne; second, to avod the pessmsm related to off-lne budget allocaton, an effcent reclamng mechansm, namely the GRUB algorthm [6], s used to explot the budget left by hgh-crtcalty tasks n favor of those low-crtcalty tasks that can stll complete wthn ther deadlne. 1 Introducton Wth the progress of computer archtectures, embedded computng systems are requred to execute more and more concurrent actvtes on the same hardware platform. In msson-crtcal systems, computatonal actvtes may have dfferent levels of crtcalty, and therefore dfferent guarantee requrements mposed by certfcaton authortes. In partcular, more crtcal tasks are requred to have more conservatve estmatons for ther computatonal requrements, wth respect to less crtcal actvtes. Such more conservatve estmatons ncrease system predctablty by over allocatng computatonal resources to more crtcal tasks, but also decrease the overall effcency. To partally compensate for such pessmstc estmatons, Vestal [16] proposed a new task model where each task can be specfed wth dfferent levels of crtcalty, each charactersed by a dfferent computaton tme estmate, dependng on the crtcalty level: the hgher the crtcalty level, the hgher the computaton tme estmate. Slghtly dfferent models have been also proposed by other authors. In ths paper, we consder a system wth two crtcalty levels that must execute a task set Γ of n perodc or sporadc tasks. Each task τ s charactersed The research leadng to these results has receved fundng from the European Unon Seventh Framework Programme (FP7/ ) under grant agreement No

2 by a crtcalty level X, whch can be ether hgh (HI) or low (LO), a worst-case computaton tme (WCET) C (whch depends on ts crtcalty level), a perod (or mnmum nterarrval tme) T, and a relatve deadlne D. Tasks wth low crtcalty,denoted aslo-tasks(τ LO ),haveasnglewcetestmatec,whereas tasks wth hgh crtcalty, denoted as HI-tasks (τ HI ), have a normal WCET estmate C and a more conservatve one, C ov, to take overruns nto account, where C ov > C. Each task generates an nfnte sequence of jobs, τ,1, τ,2,..., where each job τ,j s charactersed by a release tme r,j, a computaton tme c,j, and an absolute deadlne d,j. The actual computaton tme requested by a job τ,j s denoted by e,j. Accordng to such a model, the task set Γ s parttoned n two subsets Γ LO and Γ HI and the mxed crtcalty (MC) feasblty problem s formulated as follows: Defnton 1. A task set Γ s MC-feasble f and only f both the followng condtons are verfed: 1. If all HI-tasks execute for no more than ther optmstc computaton tme C, then there exsts a schedule where all tasks n Γ complete wthn ther deadlne. 2. If one or more HI-tasks exceed ther optmstc computaton tme C (but not ther conservatve estmate C ov ), then there exsts a schedule where all tasks n Γ HI complete wthn ther deadlne. The problem of optmally schedulng such mxed-crtcalty systems has been shown to be hghly ntractable even under very smple system models [2]. The complexty comes from the fact that optmal schedulng decsons depend on the knowledge of the actual tasks executon tmes, whch are not known off-lne, but wll be avalable only when a task completes or exceeds ts optmstc estmate. Gven such a dependency of schedulng decsons from future knowledge, t s clear that optmalty can only be acheved by an deal clarvoyant scheduler. To better clarfy ths ssue, consder the task set reported n Table 1. X C C ov T D τ 1 LO τ 2 HI Table 1. Sample mxed crtcalty task set. As llustrated n Fgure 1, the task set s MC-feasble, snce both condtons stated n Defnton 1 are verfed. Nevertheless, Fgure 2 llustrates that no onlne algorthm can guarantee the MC-schedulablty of the task set, because for each decson taken at tme t = 0 (to schedule τ 1 or τ 2 ), there exsts a stuaton n whch a task msses ts deadlne. Ths example shows that the correct decson that produces an M C- feasble schedule can be taken only by a clarvoyant scheduler that knows (at tme t = 0) how much task τ 2 wll execute.

3 τ LO 1 τ LO 1 τ HI 2 (a) τ HI 2 (b) Fg.1. If τ 2 does not exceed C 1, Γ s feasble (a), and f τ 2 executes for C ov 2, then Γ HI s feasble. τ 1 τ 1 τ 2 τ 2 (a) (b) Fg.2. If τ 1 s scheduled at t = 0, τ 2 can mss ts deadlne (a); and f τ 2 s scheduled at t = 0, τ 1 wll mss ts deadlne (b). Contrbuton In ths paper we propose a reservaton-based approach to schedule mxed crtcalty systems n a way that guarantees the schedulablty of HI-tasks ndependently of the behavor of LO-tasks. Two key deas are presented: frst, to reduce the system uncertanty and advance the tme at whch a HI-task reveals ts actual executon tme, the ntal porton of ts code s handled by a dedcated server wth a bandwdth reserved for the worst-case, but wth a shorter deadlne; second, to avod the pessmsm related to off-lne budget allocaton, an effcent reclamng mechansm, namely the GRUB algorthm [6], s used to explot the budget left by HI-tasks n favor of those LO-tasks that can stll complete wthn ther deadlne. Paper structure The rest of the paper s organzed as follows. Secton 2 formally presents the general approach. Secton 3 presents the detals of the reservaton server. Secton 4 llustrates the smulaton results obtaned wth the proposed approach. Secton 5 presents some related work. Secton 6 concludes the paper and presents some future work. 2 General approach We consder a reservaton-based real-tme system where each task (or group of tasks) can be assgned a reservaton server that allocates a budget Q every perod P. To better explot the avalable computatonal resources, we assume that all the servers are scheduled by the Earlest Deadlne Frst(EDF) schedulng algorthm [11].

4 Snce HI-tasks must be guaranteed under all operatng condtons and we cannot know n advance how much they wll execute, each HI-task τ HI s assgned a dedcated reservaton server (HI-server) wth bandwdth α HI suffcent to satsfy ts more conservatve executon tme C ov. Therefore, each HI-task s handled by a perodc reservaton (Q,P ), where Q = C ov and P = T, thus havng a bandwdth α HI = Cov. (1) T The bandwdth remanng for servng all the LO-tasks s then: α LO = 1 τ Γ HI α HI. (2) Let U LO be the total bandwdth requred by the LO-tasks, that s, U LO = τ Γ LO C T. (3) Note that, f U LO α LO, then there s enough bandwdth to complete all LO-tasks wthn ther deadlne, even when the system runs n hgh-crtcalty mode, hence the problem s trvally solved. In ths paper, we consder the more nterestng case where U LO > α LO, so that not all LO-tasks can be guaranteed to complete before ther deadlnes n all modes. Nevertheless, when the system runs n low-crtcalty mode, that s, when all the HI-tasks do not exceed ther optmstcestmatec,weproposetouseareclamngmechansmfordstrbutng the spare bandwdth saved by HI-task to LO-tasks. In partcular, whenever a HI-job τ,j HI completes before ts optmstc estmate (e,j < C ), the followng bandwdth can be reclamed: U,j rec = Cov e,j T. (4) When the system swtches to hgh-crtcalty mode, there are two ways of dealng wth LO-tasks: they may be dropped, as proposed n most of the prevous research on mxed-crtcalty schedulng, or they can contnue executng as soft real-tme tasks, wthout nterferng wth the HI-tasks. In ths paper, we adopt ths second approach. To schedule LO-tasks, we can follow two alternatve approaches: 1. All LO-tasks are assgned a sngle reservaton server (LO-server) wth bandwdth α LO. 2. Each LO-task s assgned a dfferent server such that the sum of the bandwdths of these servers does not exceed α LO. In ths paper, these two approaches are compared to see whether any one domnates the other.

5 3 Server mechansm As dscussed n the prevous secton, we assgn each HI-task a dedcated server wth bandwdth α HI suffcent to cover the largest computatonal requrements C ov of the task. At the same tme, as soon as each job of a HI-task τ completes, the remanng budget s reclamed and assgned to the LO-tasks. To be able to reclam such an extra budget n advance, we are nterested n advancng the completon tme of HI-tasks as soon as possble. To acheve ths goal, we use a technque smlar to the EDF-VD algorthm, proposed n [4,3]. Ths technque conssts n usng two dfferent deadlnes and budgets for a HI-task, dependng on whether t completes before or after ts normal worst-case executon tme C. The followng secton descrbes how to modfy the GRUB server to acheve ths objectve. 3.1 Hgh-crtcalty servers A HI-server for a HI-task τ s defned as a tuple (Q,Q ov,p ), where Q = C, Q ov = C ov, and P = T. The server s assgned a bandwdth α HI = Q ov /P suffcent to guarantee the more conservatve executon tme. At run tme, the server manages a capacty q, a vrtual tme v, a schedulng deadlne d, and a crtcalty mode γ. Moreover, the server has an nternal state whch can be IDLE, READY, EXECUTING, RECHARGING and RELEASING. The server s ntally n the IDLE state and ts crtcalty mode s γ = LO. The state dagram for the server s shown n Fgure 3. RECHARGING Budget exhausted Recharged Arrval dspatch IDLE READY EXEC preempton Vrtual fnshng fnshng RELEASING Fg. 3. State dagram for the HI-Server. A server that s not IDLE s sad to be actve. Let A be the set of actve servers. The algorthm mantans a global varable U act = α HI. (5) The server uses the followng rules: S A

6 1. When a HI-task s actvated at tme t, the server moves from the IDLE to the READY state. Correspondngly, ts budget s replenshed at q = Q and ts deadlne s set at: d = t+ Q Q ov P = t+ Q α HI = t+ q α HI Note that such a deadlne s shorter than the usual server deadlne (t+p ). Moreover, the capacty (Q = C ) s also less than the maxmum one (Q ov = C ov ). However, the server bandwdth s stll α HI. Also, the server moves to the actve set A, therefore the value of U act s updated to U act +α HI. 2. When n READY, the HI-server wth the earlest schedulng deadlne s executed and moves to EXECUTING. 3. When n EXECUTING, the server capacty s decreased as: dq = U act dt If the system s fully utlsed and all servers are actve (U act = 1), ths translates n reducng the capacty of the server at unt rate. When the system s not fully utlzed, or when some server s IDLE, the capacty s decreased as a lower rate, so that the server can actually reclam the free system bandwdth. 4. If, whle n EXECUTING, the server s preempted by another server wth earler deadlne, t moves back to READY, and ts capacty s not decremented anymore. 5. If, whle n EXECUTING, the capacty s exhausted, then the server behaves accordng to the values of the crtcalty mode: (a) Ifthecrtcaltymodeγ = LO,thenthecapactysmmedatelyrecharged to q = Q ov Q, and the deadlne s postponed to d d + Qov Q α HI = d + q α HI (Notce that ths corresponds to the deadlne of the orgnal HI-task). Also, the crtcalty level s rased to γ HI. (b) If the crtcalty mode s γ = HI, a system excepton s rased, as a HI-task should never exceed ts budget Q ov. 6. If, whle n EXECUTING, the task completes the executon of the current job, the server moves to the RELEASING state. Correspondngly, the vrtual tme s computed for the server as follows: v d q α HI 7. The server remans n state RELEASING untl t v. At that pont, the server moves to IDLE state and the crtcalty level s set to γ LO. If t > v, then an extra capacty of α HI (v t) s donated to the frst server n the ready queue. Also, the server s removed from the set of actve servers A, and the overall utlzaton s decreased to U act U act α HI...

7 3.2 Low-crtcalty servers A smlar algorthm s used for mplementng the LO-server for servng LOtasks, wth a few modfcatons to the rules. A LO-Server s defned by only two parameters, the budget Q and the perod P. As stated n Secton 2, the LO-server s assgned a bandwdth α LO gven by Equaton (2). At run-tme, the servermanagesa capactyq, a schedulng deadlne d, and has a state. The state dagram for a LO-server s the same as a HI-server, and s shown n Fgure 3. The followng rules change: 1 If the server s IDLE, when one of the LO-tasks served by the server s actvated at tme t, the server moves from IDLE to the READY state. Correspondngly, ts budget s replenshed at the value q = Q and the server deadlne s set at: d = t+p = t+ Q α LO = t+ q α LO Notce that ths s the same equaton as the HI-server. Also, the server moves to the actve set A, therefore the value of U act s updated to U act U act +α LO. 5 If, whle n EXECUTING, the capacty s exhausted, then the server moves to the RECHARGING state and a rechargng tme s set at d. The server s suspended from executon untl the capacty replenshment. 6 If, whle n EXECUTING, the task completes the executon of the current job, and there are no more tasks n the server local queue, the server moves to the RELEASING state. Correspondngly, the vrtual tme s computed for the server as follows: v d q. α LO 8 If, whle the servers n RECHARGING state, t = d, then the serverbudget s replenshed at q Q, the server deadlne s postponed at d d +P, and the server s moved to the READY state. 9 If, whle the server s n RELEASING state, a new LO-task s actvated locally n the server, then the server moves to the READY state, wth the same capacty and deadlne An example Consder a smple MC task set consstng of only two tasks: a LO-task τ 1 = (C 1 = 4,T 1 = 6) and a HI-task τ2 HI = (C 2 = 2,C2 ov = 4,T 2 = 8). To schedule ths task set, we start by defnng a HI-server S 2 = (Q 2 = 2,Q ov 2 = 4,P 2 = 8); the server bandwdth s α HI 2 = 0.5. The frst queston s: how much budget we can reserve for τ 1? Clearly, we cannot reserve (Q 1 = 4,P 1 = 6), as there s not enough bandwdth left. Therefore, the LO-server s defned wth a bandwdth α LO 1 = 1 α HI 2 = 0.5, a perod P 1 = T 1 = 6, and a budget Q 1 = α LO 1 P 1 = 3. The schedule produced by the proposed algorthm s shown n Fgure 4.

8 τ 1 τ Fg. 4. Example of reclamaton. At tme 0, task τ 2 starts executng nsde ts server. Both servers are actve (because they both arrve at tme t = 0), so the capacty s updated at the followng rate whle t executes: dq 2 dt = Uact = 1 Therefore, when task τ 2 completes, the server has budget q 2 = 0. The server moves to state RELEASING and vrtual tme s computed as v 2 = 4. Therefore, the server remans actve untl tme t = 4, and from then t becomes nactve untl tme t = 8. At tme t = 2, task τ 1 starts executng. Its budget s ntally q 1 = 3. Agan, all servers are actve (remember that Server S 2 wll become nactve at tme 4), hence capacty s decreased at unt rate. At tme t = 4, the server S 2 becomes IDLE. Therefore, the capacty rate for task τ 1 changes. Frst of all, let us observe that at tme t = 4 ts value s q 1 = 1. The new rate s: dq 2 dt = Uact = 0.5. Ths means that, at the current rate, the task can stll execute for 2 unts of tme. That s exactly what we need to complete the task at tme t = 6. At tme t = 6, the frst nstance of task τ 1 completes, but the second one s actvated. Therefore, the server rechargests budget at q 1 = 3, and contnues to execute wth deadlne at d 1 = 12. Snce the other server s stll nactve, the rates for the vrtual tme and the deadlne do not change. At tme t = 8, task τ 2 s actvated agan and S 2 becomes actve. The current value of the capacty s q 1 = 2. Suppose the scheduler decdes to contnue executng τ 1. Therefore, the new rates s now: dq 2 dt = 1 And ths means that τ 1 can execute for two more unts of tme, completng ts executng at tme t = 10. In ths example we have seen that τ 1 s able to complete executon of all ts jobs wthn ts deadlne, even f the assgned budget s less than ts executon requrements, thanks to the reclamng mechansm.

9 However, t s stll to be understood how much capacty can be reclamed by LO-tasks. In fact, t s easy to buld an example n whch the LO-server does not receve enough extra capacty to complete all ts tasks before ther deadlnes. For example, f the LO-tasks have very short relatve deadlnes compared to the HI-tasks, they wll executed before them most of the tmes, and hence they wll not be able to reclam any capacty. Computng the amount of capacty reclamed by LO-tasks s a dffcult and open problem that wll be the subject of our future research. In ths paper we just compare two methods for schedulng LO-tasks nsde a LO-server: usng a sngle server for servng all the LO-tasks; or usng a dedcated LO-server for each LO-task. 4 Expermental results To evaluate the performance of the reclamaton algorthm presented n Secton 3, we performed a set of smulaton experments. The server algorthms have been mplemented n RTSm [12], a schedulng smulaton tool for modelng real-tme systems. In each smulaton run, we generated 4 HI-tasks and 4 LO-tasks. Computaton tmes and the perods of the HI-tasks have been randomly selected to get a cumulatve utlzaton equal to 50%: Cov = 0.5. T τ ΓHI In the frst set of experments, the perods of the HI-tasks have been chosen accordng to a unform dstrbuton n the range [1000, 5000], n multples of 100. In the second set of experments, they were chosen n the nterval [6000, 10000]. Computaton tmes n low-crtcalty mode were computed as a fxed fracton of the computaton tmes n hgh-crtcalty mode: τ Γ HI C = r C ov where r was vared between [0.2, 0.75]. Computaton tmes and perods of the LO-tasks were chosen to acheve a cumulatve utlzaton equal to In ths way, for all values of parameter r, we have: C + C 1. T T τ HI τ LO In other words, we made sure that the system s never overloaded n lowcrtcalty mode. In the frst set of experments, the perods of the LO-tasks were chosen n the range [6000, 10000], whereas n the second set of experments perods were chosen n [1000, 5000]. For each HI-task we prepared a HI-server wth bandwdth α HI = C ov /T. For the LO-tasks, we made two dfferent choces: assgnng all LO-tasks to a

10 sngle LO-server wth utlzaton equal to 50% and perod P = 100; or assgn each LO-task to a dfferent LO-server wth bandwdth proportonal to ts computatonal requrements, scaled down so that the sum of the bandwdth assgned to the LO-server was 50%. In the sngle server case, LO-tasks nsde the server were scheduled by the EDF local scheduler. For each combnaton of parameters, we generated 30 dfferent task sets wth random perods and computaton tmes. Each smulaton was run for unts of smulaton tme. We only analysed the low-crtcalty mode, to test the effectveness of the reclamng algorthm n that condton. Therefore, HI-tasks never execute more than ther optmstc computaton tme C. We measured the average number of deadlnes mssed and the tardness of the LO-tasks. Smulaton results are reported n the followng sectons. 4.1 Frst set of experments In ths frst set of experments, the perods of the HI-tasks have been chosen to be alllowerthanthe perodsofthe LO-tasks.Therefore,atleastatthebegnnng of the schedule, LO-tasks execute after HI-tasks have been completed, and so they can mmedately take advantage of the reclamed bandwdth. The deadlne mss percentage of the LO-tasks s shown n Fgure 5 for the case of separate servers, and sngle server. It s evdent that the deadlne mss percentage s very low n all cases. Even for the case of r = 0.75 (where the total system utlzaton s very close to 100%), t never goes above 5% of the total number of deadlnes. Also notce that puttng all LO-tasks n a sngle server s very effectve, as we observed 0 deadlnes mssed n all the experments Deadlne Msses of LO-tasks Separate Servers Sngle Server % Deadlne Mss Rato of executon LO/HI of HI-tasks Fg.5. Deadlne mss percentage of LO-tasks, usng dedcated servers, or a sngle cumulatve server. The LO-tasks have larger perods than the HI-tasks.

11 A very smlar trend can be observed for the tardness reported n Fgure 6. Such small values of the tardness ndcate that the reclamng mechansm s very effectve, even wth very hghly loaded systems Tardness of LO-tasks Separate Servers Sngle Server Tardness Rato of executon LO/HI of HI-tasks Fg. 6. Tardness of LO-tasks, usng dedcated servers or a sngle cumulatve server. The LO-tasks have larger perods than the HI-tasks. 4.2 Second set of experments In ths second set of experments, the perods of the HI-tasks have been chosen to be all hgher than the perods of the LO-tasks. Therefore, at least at the begnnng of the schedule, LO-tasks execute before HI-tasks, so they cannot mmedately take advantage of the reclamed bandwdth. The deadlne mss percentage of the LO-tasks s shown n Fgure 7 for the case of separate servers and sngle server. Onceagan,averysmlartrendcan be observedforthe tardnessn Fgure8. Notce that n ths case we detected very small values of the tardness for r 0.6 due to a very small number of deadlne msses (not vsble n the graphs). Whle these smulatons cannot conclusvely establsh the theoretcal performance guarantees for LO-tasks, they ndcate that t s ndeed worthwhle to perform further nvestgaton on reclamaton technques for mxed crtcalty systems. 5 Related work The problem of schedulng mxed crtcalty systems has been addressed by several authors under slghtly dfferent models and assumptons. Lakshmanan et al.[5,8,9] proposed a slack-aware approach on top of fxed prorty schedulng, provdng a schedulablty test that guarantees that all deadlnes

12 Deadlne Msses of LO-tasks Separate Servers Sngle Server 0.1 % Deadlne Mss Rato of executon LO/HI of HI-tasks Fg.7. Deadlne mss percentage of LO-tasks, usng dedcated servers, or a sngle cumulatve server. The LO-tasks have smaller perods than the HI-tasks Tardness of of LO-tasks Separate Servers Sngle Server Tardness Rato of executon LO/HI of HI-tasks Fg. 8. Tardness of LO-tasks, usng dedcated servers or a sngle cumulatve server. The LO-tasks have smaller perods than the HI-tasks.

13 of HI-tasks are met regardless of the runtme behavor of LO-tasks, provded the executon of at most one HI-task overruns ts lower WCET estmate. Baruah et. al. [1] proposed an effectve algorthm, called OCBP (Own Crtcalty Based Prorty), to schedule a set of non-recurrent jobs. Although OCBP s able to acheve the hghest speedup factor among all the fxed-job-prorty algorthms, t cannot be appled to recurrent tasks. LandBaruah[10]proposedanalgorthm,referredtoasLB,toextendOCBP to sporadc tasks, but t reles on very pessmstc schedulablty tests based on load bound condtons. Moreover, t ntroduces large run-tme overhead as t needs on-lne pseudo-polynomal prorty assgnment recomputaton. To overcome the lmtatons oflb,guan et al. [7] presentedanew algorthm,referredto as PLRS(Prorty Lst Reuse Schedulng) to schedule certfable mxed-crtcalty sporadc task systems. Pellzzon et al. [13] proposed a reservatons-based approach to ensure strong solaton among subsystems of dfferent crtcalty. Petters et. al. [14] also consdered the use of temporal solaton of subsystems for mxed-crtcalty systems, and addressed many practcal ssues n buldng such systems n realty. In general, the drawback of the resource/temporal solaton approach s that t reles on severely over-provsonng computng resources, whch may result n sgnfcant cost and energy waste. Baruah et al. proposed the EDF-VD algorthm [3,4], whch s smlar to the server mechansm proposed n ths paper. In partcular, they propose to antcpate the deadlnes of HI-tasks so that when executng n LO-crtcalty mode ther completon s antcpated. Ther formula for computng the antcpated deadlne s global,.e. t reles on the global utlsaton of HI-tasks, whereas n ths paper we propose a dfferent formula that accounts for the bandwdth of each dfferent HI-task separately and ndependently. In [3], the authors also propose a test for checkng the schedulablty of LO-tasks n LO-crtcalty mode, and compute the speed-up factor of ther algorthm to be 4/3. Santy et al. [15] propose an algorthm for lettng some of the LO-crtcalty task execute even after the system has swtched to HI-crtcalty mode, as long as ther executon does not compromse the schedulablty of HI-tasks. Also, they propose a method to reset the system crtcalty level at certan specfed dle ntervals. In ths paper, we also propose to contnue executng LO-crtcalty tasks as soft real-tme tasks even after the system swtches to HI-crtcalty: the temporal solaton mechansm guarantees that the HI-tasks wll not be nfluenced. 6 Conclusons We presented a reservaton-based approach to schedule mxed crtcalty systems n a way that guarantees the schedulablty of hgh-crtcalty tasks ndependently of the behavor of low-crtcalty tasks. Pessmsm related to off-lne budget allocaton s avoded by an effcent reclamng mechansm that explots the budget left by hgh-crtcalty tasks for those actve low-crtcalty tasks that can stll complete wthn ther deadlnes.

14 We are currently nvestgatng a test for guaranteeng the schedulablty of LO-tasks n LO-crtcalty mode, by computng a lower bound on the amount of reclamng avalable n any tme nterval. We wll then compare the schedulablty test wth the one proposed n [3] to evaluate the performance of the two approaches. References 1. S. Baruah, H. L, and L. Stouge. Towards the desgn of certfable mxed-crtcalty systems. In Proceedngs of the 16th IEEE Real-Tme and Embedded Technology and Applcatons Symposum (RTAS 2010), Sanjoy Baruah, Vncenzo Bonfac, Ganlorenzo D Angelo, Haohan L, Alberto Marchett-Spaccamela, Ncole Megow, and Leen Stouge. Schedulng real-tme mxed-crtcalty jobs. IEEE Transactons on Computers, 61(8): , Sanjoy K. Baruah, Vncenzo Bonfac, Ganlorenzo D Angelo, Haohan L, Alberto Marchett-Spaccamela, Suzanne van der Ster, and Leen Stouge. The preemptve unprocessor schedulng of mxed-crtcalty mplct-deadlne sporadc task systems. In ECRTS 12, pages , Sanjoy K. Baruah, Vncenzo Bonfac, Ganlorenzo D Angelo, Alberto Marchett- Spaccamela, Suzanne Van Der Ster, and Leen Stouge. Mxed-crtcalty schedulng of sporadc task systems. In Proceedngs of the 19th European conference on Algorthms, ESA 11, pages , Berln, Hedelberg, Sprnger-Verlag. 5. D. de Nz, K. Lakshmanan, and R. Rajkumar. On the schedulng of mxedcrtcalty real-tme task sets. In Proceedngs of the 30th IEEE Real-Tme Systems Symposum (RTSS 2009), December G.Lpar and S.K. Baruah. Greedy reclamaton of unused bandwdth n constant bandwdth servers. In IEEE Proceedngs of the 12th Euromcro Conference on Real-Tme Systems, Stokholm, Sweden, June Nan Guan, Pontus Ekberg, Martn Stgge, and Wang Y. Effectve and effcent schedulng of certfable mxed-crtcalty sporadc task systems. In Proceedngs of the 32nd IEEE Real-Tme Systems Symposum (RTSS 2011), K. Lakshmanan, D. de Nz, and R. Rajkumar. Resource allocaton n dstrbuted mxed-crtcalty cyber-physcal systems. In Proceedngs of the 30th Internatonal Conference on Dstrbuted Computng Systems (ICDCS 2010), K. Lakshmanan, D. de Nz, and R. Rajkumar. Mxed-crtcalty task synchronzaton n zero-slack schedulng. In Proceedngs of the 17th IEEE Real-Tme and Embedded Technology and Applcatons Symposum (RTAS 2011), H. L and S. Baruah. An algorthm for schedulng certfable mxedcrtcalty sporadc task systems. In Proceedngs of the 31st IEEE Real-Tme Systems Symposum (RTSS 2010), December C.L. Lu and J.W. Layland. Schedulng algorthms for multprogrammng n a hard-real-tme envronment. Journal of the Assocaton for Computng Machnery, 20(1):46 61, January Lug Palopol, Guseppe Lpar, Luca Aben, Marco D Natale, Paolo Anclott, and Fabo Contcell. A tool for smulaton and fast prototypng of embedded control systems. In Seongsoo Hong and Santosh Pande, edtors, LCTES/OM, pages ACM, R. Pellzzon, P. Meredth, M.Y. Nam, M. Sun, M. Caccamo, and L. Sha. Handlng mxed crtcalty n soc-based real-tme embedded systems. In Proceedngs of the ACM Internatonal Conference on Embedded Software (EMSOFT 2009), 2009.

15 14. S. Petters, M. Lawtzky, R. Heffernan, and K. Elphnstone. Towards real multcrtcalty schedulng. In 15th IEEE Internatonal Conference on Embedded and Real-Tme Computng Systems and Applcatons (RTCSA 2009), Franços Santy, Laurent George, Ph. Therry, and Joël Goossens. Relaxng mxedcrtcalty schedulng strctness for task sets scheduled wth fp. In IEEE Computer Socety, edtor, ECRTS, pages , July Steve Vestal. Preemptve schedulng of mult-crtcalty systems wth varyng degrees of executon tme assurance. In Proceedngs of the 28th IEEE Real-Tme Systems Symposum (RTSS 2007), pages , December 2007.