Limited Preemptive Scheduling for Real-Time Systems: a Survey

Transcription

1 Lmted Preemptve Schedulng for Real-Tme Systems: a Survey Gorgo C. Buttazzo, Fellow Member, IEEE, Marko Bertogna, Senor Member, IEEE, and Gang Yao Abstract The queston whether preemptve algorthms are better than non-preemptve ones for schedulng a set of real-tme tasks has been debated for a long tme n the research communty. In fact, especally under fxed prorty systems, each approach has advantages and dsadvantages, and no one domnates the other when both predctablty and effcency have to be taken nto account n the system desgn. Recently, lmted preempton models have been proposed as a vable alternatve between the two extreme cases of fully preemptve and non-preemptve schedulng. Ths paper presents a survey of the exstng approaches for reducng preemptons and compares them under dfferent metrcs, provdng both qualtatve and quanttatve performance evaluatons. Index Terms Real-tme systems, Non-preemptve regons, Lmted-preemptve schedulng. I. INTRODUCTION PREEMPTION s a key factor n real-tme schedulng, snce t allows the operatng system to mmedately allocate the processor to ncomng tasks requrng urgent servce. In fully preemptve systems, the runnng task can be nterrupted at any tme by another task wth hgher prorty, and be resumed to contnue when all hgher prorty tasks have completed. In other systems, preempton may be dsabled for certan ntervals of tme durng the executon of crtcal operatons (e.g., nterrupt servce routnes, crtcal sectons, etc.). In other stuatons, preempton can be completely forbdden to avod unpredctable nterference among tasks and acheve a hgher degree of predctablty (although hgher blockng tmes). The queston whether enablng or dsablng preempton durng task executon has been nvestgated by many authors under several ponts of vew and t s not trval to answer. A general dsadvantage of the non-preemptve dscplne s that t ntroduces addtonal blockng tme n hgher prorty tasks, so reducng schedulablty. On the other hand, there are several advantages to be consdered when adoptng a non-preemptve scheduler. In partcular, the followng ssues have to be taken nto account when comparng the two approaches: In many practcal stuatons, such as I/O schedulng or communcaton n a shared medum, ether preempton s mpossble or prohbtvely expensve []. Gorgo C. Buttazzo s wth the Scuola Superore Sant Anna, Psa, Italy. E-mal: g.buttazzo@sssup.t. Marko Bertogna s wth the Unversty of Modena and Reggo Emla, Italy. E-mal: marko.bertogna@unmore.t Gang Yao s wth the Unversty of Illnos at Urbana Champagn. E-mal: gangyao@llnos.edu. Copyrght (c) 2009 IEEE. Personal use of ths materal s permtted. However, permsson to use ths materal for any other purposes must be obtaned from the IEEE by sendng a request to pubs-permssons@eee.org. Preempton destroys program localty, ncreasng the runtme overhead due to cache msses and pre-fetch mechansms. As a consequence, worst-case executon tmes (WCETs) are more dffcult to characterze and predct [2], [3], [4], [5]. Mutual excluson s trval n non-preemptve schedulng, whch naturally guarantees the exclusve access to shared resources. On the contrary, to avod unbounded prorty nverson [6], preemptve schedulng requres the mplementaton of specfc concurrency control protocols for accessng shared resources [6], [7], whch ntroduce addtonal overhead and complexty. In control applcatons, the nput-output delay and jtter are mnmzed for all tasks when usng a non-preemptve schedulng dscplne, snce the nterval between start tme and fnshng tme s always equal to the task computaton tme [8]. Ths smplfes control technques for delay compensaton at desgn tme. Non-preemptve executon allows usng stack sharng technques [7] to save memory space n small embedded systems wth strngent memory constrants [9], [0]. In summary, arbtrary preemptons can ntroduce a sgnfcant runtme overhead and may cause hgh fluctuatons n task executon tmes, so degradng system predctablty. In partcular, at least four dfferent types of costs need to be taken nto account at each preempton: ) Schedulng cost. It s the tme taken by the schedulng algorthm to suspend the runnng task, nsert t nto the ready queue, swtch the context, and dspatch the new ncomng task. 2) Ppelne cost. It accounts for the tme taken to flush the processor ppelne when the task s nterrupted and the tme taken to refll the ppelne when the task s resumed. 3) Cache-related cost. It s the tme taken to reload the cache lnes evcted by the preemptng task. Bu et al. [] showed that on a PowerPC MPC740 wth 2 MByte two-way assocatve L2 cache the WCET ncrement due to cache nterference can be as large as33% of the WCET measured n non-preemptve mode. 4) Bus-related cost. It s the extra bus nterference for accessng the RAM due to the addtonal cache msses caused by preempton. The cumulatve executon overhead due to the combnaton of these effects s referred to as Archtecture related cost. Unfortunately, ths cost s characterzed by a hgh varance and depends on the specfc pont n the task code where preempton takes place [2], [3], [4]. The total ncrease of the worst-case executon tme of a task τ s also a functon of the total number of preemptons exper-

2 2 enced by τ, whch n turn depends on the task set parameters, on the actvaton pattern of hgher prorty tasks, and on the specfc schedulng algorthm. Such a crcular dependency of WCET and number of preemptons makes the problem not easy to be solved. The major contrbuton of ths paper s to provde a detaled comparson of the varous lmted preemptve approaches proposed n the lterature, wth respect to fully preemptve and non-preemptve schemes. Schedulablty tests for each method are reported for completeness, and smulaton experments are carred out to evaluate the mpact of the algorthms on the number of preemptons and the overall system schedulablty. The results reported here can be used to select the most approprate schedulng scheme to ncrease the effcency of tme-crtcal embedded systems wthout sacrfcng predctablty. The rest of the paper s organzed as follows. Secton II descrbes three dfferent approaches proposed n the lterature to handle lmted preemptve schedulng. Secton III descrbes the task model and the termnology adopted n the paper. Secton IV presents the schedulablty analyss for the non-preemptve task model. The preempton thresholds model s analyzed n Secton V. Secton VI detals the deferred preempton model, whle the method of fxed preempton ponts s analyzed n Secton VII. Consderatons regardng the dfferences between the varous models are presented n Secton VIII. Secton IX reports and dscusses some smulaton results and Secton X states our conclusons. II. LIMITED PREEMPTIVE APPROACHES Often, preempton s consdered a pre-requste to meet tmng requrement n real-tme system desgn; however, n most cases, a fully preemptve scheduler produces many unnecessary preemptons. To reduce the runtme overhead due to preemptons and stll preserve the schedulablty of the task set, the followng approaches have been proposed n the lterature: Preempton Thresholds Schedulng (PTS). Ths approach, proposed by Wang and Saksena [5], allows a task to dsable preempton up to a specfed prorty level, called preempton threshold. Thus, each task s assgned a regular prorty and a preempton threshold, and the preempton s allowed to take place only when the prorty of the arrvng task s hgher than the threshold of the runnng task. Deferred Preemptons Schedulng (DPS). Accordng to ths method, frst ntroduced by Baruah [6] under EDF, each task τ specfes the longest nterval q that can be executed non-preemptvely. For the sake of clarty, t s worth notng that the termnology s not consstent n the lterature, snce other authors (e.g., Burns [7] and Brl et al. [8]) used the term Deferred Preemptons to actually denote Fxed Preempton Ponts. However, we beleve the term Deferred s more approprate n ths case, because preempton s postponed for a gven amount of tme, rather than moved to a specfc poston n the code. Dependng on how nonpreemptve regons are mplemented, ths model can come n two slghtly dfferent versons: ) Floatng model. In ths model, non-preemptve regons are defned by the programmer by nsertng specfc prmtves n the task code that dsable and enable preempton. However, snce the start tme of each regon s not specfed n the model, nonpreemptve regons cannot be dentfed off-lne and, for the sake of the analyss, they are consdered to be floatng n the code, wth a duraton not exceedng q. 2) Actvaton-trggered model. In ths model, nonpreemptve regons are trggered by the arrval of a hgher prorty task and programmed by a tmer to last exactly for q unts of tme (unless the task fnshes earler), after whch preempton s enabled. Once a tmer s set at tme t, addtonal actvatons arrvng before the tmeout (t+q ) do not postpone the preempton any further. Once a preempton takes place, a new hgh-prorty arrval can trgger another non-preemptve regon. Fxed Preempton Ponts (FPP). Accordng to ths approach, proposed by Burns [7], a task mplctly executes n non-preemptve mode and preempton s allowed only at predefned locatons nsde the task code, called preempton ponts. In ths way, a task s dvded nto a number of non-preemptve chunks (also called subjobs). If a hgher prorty task arrves between two preempton ponts of the runnng task, preempton s postponed untl the next preempton pont. Ths approach s also referred to as Cooperatve schedulng, because tasks cooperate to offer sutable preempton ponts to mprove schedulablty. III. TERMINOLOGY AND NOTATION Let us consder a set of n perodc or sporadc real-tme tasks that need to be scheduled on a sngle processor. Each task τ s characterzed by a worst-case executon tme (WCET) C, a relatve deadlne D, and a perod (or mnmum nter-arrval tme) T. A constraned deadlne model s adopted, so D s assumed to be less than or equal to T. Each task s assgned a fxed prorty P, used to select the runnng task among those tasks ready to execute (a hgher value of P corresponds to a hgher prorty). Notce that task actvaton tmes are not known a pror and the actual executon tme of a task can be less than or equal to ts worst-case value C. Tasks are ndexed by decreasng prorty,.e., < n : P > P +. Addtonal termnology wll be ntroduced below for each specfc method. A. Integer tme model In real-tme operatng systems, tme nstants and nterval duratons are measured by countng the number of clock cycles generated by a real-tme clock, hence all tmng values have a resoluton equal to one clock cycle. Therefore, to use analytcal results n a real embedded system, all tmng parameters are assumed to be non-negatve nteger values. To comply wth such a conventon, all cted results derved under the doman of real numbers have been adapted to the nteger tme model. B. Crtcal nstant The maxmum response tme of each task s derved under the worst-case arrval pattern that leads to the largest nterference on

3 3 the consdered task. Such a partcular scenaro s often referred to as the crtcal nstant. For fully preemptve fxed prorty systems, Lu and Layland [9] proved that the crtcal nstant for a task occurs when t arrves synchronously wth all hgher prorty tasks, and all task nstances are released as soon as possble,.e., n a strctly perodc fashon. In the presence of non-preemptve regons, however, the addtonal blockng from lower prorty tasks has to be taken nto account, hence the crtcal nstant for a task τ occurs when t s released synchronously and perodcally wth all hgher prorty tasks, whle the lower prorty task that s responsble of the largest blockng tme of τ s released one unt of tme before τ [20]. However, the largest response tme of a task s not necessarly due to the frst job after a crtcal nstant, but mght be due to later jobs, as explaned later on. All schedulablty tests hereafter presented have been derved by computng the worst-case response tme of a task under the above descrbed noton of crtcal nstant. C. Motvatng example To better apprecate the mportance of lmted preemptve schedulng and to better understand the dfference among the lmted preemptve approaches presented n ths survey, Table I reports a sample task set that wll be used as a common example throughout ths paper, because t results to be unschedulable by Deadlne Monotonc [2], both n fully preemptve and n fully non-preemptve mode, but t can be schedulable by all lmted preemptve approaches. C T D τ 6 4 τ τ TABLE I PARAMETERS OF A SAMPLE TASK SET. Fgure llustrates the schedule produced by Deadlne Monotonc n fully preemptve mode. As clear from the fgure, the task set s not feasble, snce task τ 3 msses ts deadlne. τ start at least one unt before the crtcal nstant. Such a blockng term ntroduces an addtonal delay before task executon, whch could jeopardze schedulablty. Hgh prorty tasks are those that are most affected by such a blockng delay, snce the maxmum n Equaton () s computed over a larger set of tasks. Fgure 2 llustrates the schedule generated by Deadlne Monotonc on the task set of Table I when preemptons are dsabled. Wth respect to the schedule shown n Fgure, notce that τ 3 s now able to complete before ts deadlne, but the task set s stll not schedulable, snce now τ msses ts deadlne. τ τ 2 τ deadlne mss Fg. 2. Schedule produced by non-preemptve Deadlne Monotonc on the task set of Table I. Unfortunately, under non-preemptve schedulng, the least upper bounds of both Rate Monotonc (RM) [9] and Earlest Deadlne Frst (EDF) [9] drop to zero! Ths means that there exst task sets wth arbtrary low utlzaton that cannot be scheduled by RM and EDF when preemptons are dsabled. A. Feasblty analyss The feasblty analyss of non-preemptve task sets s more complex than under fully preemptve schedulng. Davs et al. [22] showed that n non-preemptve schedulng the largest response tme of a task does not necessarly occur n the frst job, after the crtcal nstant. An example of such a stuaton s llustrated n Fgure 3, where the worst-case response tme of τ 3 occurs n ts second nstance. Such a schedulng anomaly, dentfed as self-pushng phenomenon, occurs because the hgh prorty jobs actvated durng the non-preemptve executon of τ s frst nstance are pushed ahead to successve jobs, whch then may experence a hgher nterference. τ 2 3 (C,T ) τ 3 6 deadlne mss τ (3,8) Fg.. Schedule produced by Deadlne Monotonc (n fully preemptve mode) on the task set of Table I. IV. NON-PREEMPTIVE SCHEDULING (NPS) The most effectve way to reduce preempton cost s to dsable preemptons completely. In ths condton, however, each task τ can experence a blockng tme B equal to the longest computaton tme among the tasks wth lower prorty. That s, B = max {C j } () j:p j<p where the maxmum of an empty set s assumed to be zero. Notce that one unt of tme s subtracted from the computaton tme of the blockng task to consder that, to block τ, t must τ 2 (3,9) deadlne mss τ 3 (3,2) τ 4 (2,00) Fg. 3. An example of self-pushng phenomenon occurrng on task τ 3. The presence of the self-pushng phenomenon n nonpreemptve schedulng mples that the response tme analyss for a task τ cannot be lmted to ts frst job, actvated at the crtcal nstant, as done n preemptve schedulng, but t must be performed for multple jobs, untl the processor fnshes executng tasks wth prorty hgher than or equal to P. Hence,

4 4 the response tme of a task τ needs to be computed wthn the longest Level- Actve Perod, defned as follows [20]: Defnton. The Level- pendng workload W p (t) at tme t s the amount of processng that stll needs to be performed at tme t due to jobs wth prorty hgher than or equal to P released strctly before t. Defnton 2. A Level- Actve Perod L s an nterval [a,b) such that the Level- pendng workload W p (t) s postve for all t (a,b) and null n a and b. The longest Level- Actve Perod can be computed by the followng recurrent relaton: = B +C L (s) = B + L (0) h:p h P L (s ) C h. In partcular, L s the smallest value for whch L (s) = L (s ). Ths means that the response tme of task τ must be computed for all jobs τ,k, wth k [,K ], where: L K =. (3) For a generc jobτ,k, the start tmes,k can then be computed consderng the blockng tme B, the computaton tme of the precedng (k ) jobs and the nterference of the tasks wth prorty hgher than P. Hence, s,k can be computed wth the followng recurrent relaton: s (0),k = B + h:p h >P C h s (l),k = B +(k )C + T h:p h >P ( s (l ),k + ) C h. Note that the orgnal result derved n [20] adopted two dfferent expressons: one for the n-th task, that does not experence any blockng, and one for the remanng tasks. Instead, usng an nteger tme model and computng the blockng term wth Equaton (), t s possble to smplfy the analyss, usng a homogeneous formulaton for all tasks. Snce, once started, the task cannot be preempted, the fnshng tme f,k can be computed as f,k = s,k +C. (5) Hence, the response tme of task τ s gven by R = max k [,K ] {f,k (k )T }. (6) Once the response tme of each task s computed, the task set s feasble f and only f (2) (4) =,...,n R D. (7) Yao, Buttazzo, and Bertogna [23] showed that the analyss of non-preemptve tasks can be reduced to analyzng a sngle job, under specfc (but not too restrctve) condtons. The followng theorem, orgnally stated for the fxed preempton model, s presented here for the non-preemptve schedulng model, whch s a specal case of the fxed preempton model. Theorem (from [23]). The worst-case response tme of a nonpreemptve task occurs n the frst job after ts crtcal nstant f the followng two condtons are both satsfed: ) the task set s feasble under preemptve schedulng; 2) relatve deadlnes are less than or equal to perods. Under these condtons, the longest relatve start tme S of task τ s equal to s, and can be computed from Equaton (4) for k = : S (0) = B + S (l) h:p h >P C h = B + h:p h >P ( Hence, the response tme R s smply: ) S (l ) + C h. (8) R = S +C. (9) V. PREEMPTION THRESHOLDS SCHEDULING (PTS) Accordng to ths model, proposed by Wang and Saksena [5], each task τ s assgned a nomnal prorty P (used to enqueue the task nto the ready queue and to preempt) and a preempton threshold θ P (used for task executon). Then, τ can be preempted by τ h only f P h > θ. At the actvaton tme r,k, the prorty of τ s set to ts nomnal value P, so t can preempt all the tasks τ j wth threshold θ j < P. The nomnal prorty s mantaned as long as the task s kept n the ready queue. Durng ths nterval, τ can be delayed by all tasksτ h wth prortyp h > P and by at most one lower prorty task τ l wth threshold θ l P. When all such tasks complete (at tme s,k ), τ s dspatched for executon and ts prorty s rased at ts threshold level θ untl the task termnates (at tme f,k ). Durng ths nterval, τ can be preempted by all tasks τ h wth prorty P h > θ. Notce that, when τ s preempted, ts prorty s kept to ts threshold level. Preempton threshold can be consdered as a trade-off between fully preemptve and fully non-preemptve schedulng. Indeed, f each threshold prorty s set equal to the task nomnal prorty, the scheduler behaves lke a fully preemptve scheduler; whereas, f all thresholds are set to the maxmum prorty, the scheduler runs n a non-preemptve fashon. Wang and Saksena also showed that, by approprately settng the thresholds, the system can mprove the schedulablty compared wth fully preemptve and fully non-preemptve schedulng. For example, f prortes are assgned as P = 3, P 2 = 2, and P 3 =, and thresholds as θ = 3, θ 2 = 3, and θ 3 = 2, the task set of Table I results to be schedulable, and the schedule produced n the synchronous perodc arrval pattern s llustrated n Fgure 4. Notce that, at t = 6, τ can preempt τ 3 snce P > θ 3. However, at t = 0, τ 2 cannot preempt τ 3, beng P 2 = θ 3. Smlarly, at t = 2, τ cannot preempt τ 2, beng P = θ 2. A. Feasblty analyss Under fxed prortes, the feasblty analyss of a task set wth preempton thresholds can be performed by the test derved by Keskn et al. [24]. Frst of all, a task τ can be blocked only by lower prorty tasks that cannot be preempted by t, that s, The orgnal analyss by Wang and Saksena [5] has been corrected by Regehr [25], whch n ts turn has been mproved by Keskn et al. [24].

5 5 τ τ 2 τ Fg. 4. Schedule produced by Deadlne Monotonc on the task set n Table I wth prortes P = 3, P 2 = 2, and P 3 =, and thresholds θ = 3, θ 2 = 3, and θ 3 = 2. by tasks τ j wth P j < P and θ j P. Hence, a task τ can experence a blockng tme equal to the longest computaton tme among the tasks wth prorty lower than P and threshold hgher than or equal to P. That s, B = max{c j P j < P θ j } (0) j where the maxmum of an empty set s assumed to be zero. Then, the response tme R of task τ s computed by consderng the blockng tme B, the nterference before ts start tme (due to the tasks wth prorty hgher than P ), and the nterference after ts start tme (due to tasks wth prorty hgher than θ ). The analyss must be carred out wthn the longest Level- actve perod L defned n Equaton (2). Ths means that the response tme of task τ must be computed for all the jobs τ,k wth k [,K ], where K s defned n Equaton (3). For a generc job τ,k, the start tme s,k can be computed consderng the blockng tme B, the computaton tme of the precedng (k ) jobs, and the nterference of the tasks wth prorty hgher than P. Hence, s,k can be computed usng Equaton (4). The fnshng tme f,k can be computed by summng to the start tme s,k the computaton tme of job τ,k, and the nterference of the tasks that can preempt τ,k (those wth prorty hgher than θ ). That s, f (0),k = s,k+c,k = s,k+c + f (l) h:p h >θ ( f (l ),k ( s,k +) ) C h. () Agan, the nteger tme model adopted n ths paper, along wth the conventon on the blockng term gven by Equaton (0), allow smplfyng the analyss wth respect to [24], wthout needng to use two dfferent expressons for the cases wth and wthout blockng. The response tme of task τ can then be computed usng Equaton (6), and the task set s feasble f and only f Condton (7) s satsfed. be computed as R (0) = S +C + C h h:p h >θ R (l) = S +C + ( R (l ) h:p h >θ B. Selectng preempton thresholds ( S +) ) C h. (2) The example llustrated n Fgure 4 shows that a task set unfeasble under both preemptve and non-preemptve schedulng can be feasble under preempton thresholds, for a sutable settng of threshold levels. Gven a task set that s feasble under preemptve schedulng, an nterestng problem s to determne the thresholds that lmt preempton as much as possble, wthout jeopardzng the schedulablty of the task set. Saksena and Wang [26] proposed an algorthm to ncrease the threshold of each task up to the level after whch the schedule would become nfeasble. The algorthm consders one task at the tme, startng from the hghest prorty task. VI. DEFERRED PREEMPTIONS SCHEDULING (DPS) Accordng to ths method, each task τ defnes a maxmum nterval of tme q n whch t can execute non-preemptvely. Dependng on the specfc mplementaton, the non-preemptve nterval can start after the nvocaton of a system call nserted at the begnnng of a non-preemptve regon (floatng model), or can be trggered by the arrval of a hgher prorty task (actvaton-trggered model). Under the floatng model, preempton s resumed by another system call, nserted at the end of the regon (at most q unts long); whereas, under the actvaton-trggered model, preempton s enabled by a tmer nterrupt after exactly q unts (unless the task completes earler). For example, consderng the same task set of Table I, assgnng q 2 = 2 and q 3 =, the schedule produced by Deadlne Monotonc wth deferred preemptons under the actvaton-trggered model s feasble, as llustrated n Fgure 5. Dark regons represent ntervals executed n nonpreemptve mode, trggered by the arrval of hgher prorty tasks. τ τ 2 τ Fg. 5. Schedule produced by Deadlne Monotonc wth deferred preemptons for the task set reported n Table I, wth q 2 = 2 and q 3 =. The feasblty analyss under preempton thresholds can also be smplfed under the condtons of Theorem. In ths case, we have that the worst-case start tme s computed usng Equaton (8), and the worst-case response tme of task τ can A. Feasblty analyss In the presence of non-preemptve ntervals, a task can be blocked when, at ts arrval, a lower prorty task s runnng n

6 6 non-preemptve mode. Snce each task can be blocked at most once by a sngle lower prorty task, B s equal to the longest non-preemptve nterval belongng to tasks wth lower prorty. In partcular, the blockng factor can be computed as B = max {q j }. (3) j:p j<p Note that, under the floatng model, one unt of tme must be subtracted from q j to allow the non-preemptve regon to start before τ. Under the actvaton-trggered model, however, there s no need to subtract one unt of tme from q j, snce the nonpreemptve nterval s programmed to be exactly q j from the arrval tme of a hgher prorty task. In both the floatng and actvaton-trggered cases, the start tmes of non-preemptve ntervals are assumed to be unknown a pror. Therefore, non-preemptve regons cannot be dentfed off-lne and, for the sake of the analyss, they are consdered to occur n the worst possble tme (n the sense of schedulablty). Then, schedulablty can be checked through the classc response tme analyss: R = B + h:p h P R C h. (4) Note that, under the floatng model, the analyss does not need to be carred out wthn the longest Level- actve perod. In fact, the worst-case nterference onτ occurs n the frst nstance assumng that τ could be preempted one tme-unt before ts completon. On the other hand, the analyss s more pessmstc under the actvaton-trggered model, where non-preemptve ntervals are exactly equal to q unts and can last untl the end of the task. In ths case, the analyss does not take advantage of the fact that τ cannot be preempted when hgher perodc tasks arrve q unts (or less) before ts completon. The advantage of such a pessmsm, however, s that the analyss s much smpler and can be lmted to the frst job of each task. Under these assumptons, a task set s feasble wth deferred preemptons only f the task set s feasble preemptvely. The analyss of perodc tasks wth floatng non-preemptve regons has also been developed under EDF [27], [28]. B. Longest non-preemptve nterval When usng the deferred preempton method, an nterestng problem s to fnd the longest non-preemptve nterval Q for each task τ that can stll preserve the task set schedulablty. More precsely, the problem can be stated as follows: Gven a set of n perodc tasks that s feasble under preemptve schedulng, fnd the longest nonpreemptve nterval of length Q for each task τ, so that τ can contnue to execute for Q unts of tme n non-preemptve mode, wthout volatng the schedulablty of the orgnal task set. Ths problem has been solved under EDF by Bertogna and Baruah [27], and under fxed prortes by Yao et al. [29]. The soluton s based on the concept of blockng tolerance β, for a task τ, defned as follows: Defnton 3. The blockng tolerance β of a task τ s the maxmum amount of blockng τ can tolerate wthout mssng any of ts deadlnes. When deadlnes are equal to perods, a smple way to compute a lower bound on the blockng tolerance s from the Lu and Layland test [9], whch, n the presence of blockng factors, becomes: C h =,...,n + B U lub () T h:p h P where U lub () = (2 / ). Isolatng the blockng factor, the test can also be rewrtten as: B T U lub (). C h h:p h P Hence, consderng nteger computatons, we have: β = T U lub (). (5) C h h:p h P When deadlnes are less than or equal to perods, an exact bound for β can nstead be acheved by usng the schedulablty test presented n [30], so that a task set s schedulable wth deferred preemptons f and only f for each task τ : t T S(τ ) : B + t C h t, (6) where h:p h P T S(τ ) def = P (D ) (7) and P (t) s defned by the followng recurrent expresson: { P0 (t) = {t} ( t (8) P (t) = P T ) P (t). T Ths leads to the followng result [29]: B max t T S(τ ) t t h:p h P β = max t T S(τ ) t t h:p h P C h C h.. (9) Gven the blockng tolerance, the feasblty test can also be expressed as follows: =,...,n B β and, by Equaton (3), we can wrte: =,...,n max j:p j<p {q j } β. Ths mples that, to acheve feasblty, we must have: =,...,n q mn k:p k >P {β k +} Hence, the longest non-preemptve nterval Q that preserves feasblty for each task τ s: Q = mn k:p k >P {β k +}. (20) The Q terms can also be computed more effcently, startng from the hghest prorty task (τ ) and proceedng wth decreasng prorty order, accordng to the followng theorem:

7 7 Theorem 2 (from [29]). The longest non-preemptve nterval Q of task τ that preserves feasblty can be computed as Q = mn{q,β +} (2) where Q = and β = D C. Note that, n order to apply Theorem 2, Q s not constraned to be less than or equal to C, but a value of Q greater than C means that τ can be fully executed n non-preemptve mode. VII. FIXED PREEMPTION POINTS (FPP) Accordng to ths model, each task τ s splt nto m nonpreemptve chunks (subjobs), obtaned by nsertng m preempton ponts n the code. Thus, preemptons can only occur at the subjobs boundares. All the jobs generated by one task have the same subjob dvson. The k th subjob has a worstcase executon tme q,k, hence C = m k= q,k. Among all the parameters descrbng the subjobs of a task, two values are of partcular mportance for achevng a tght schedulablty result: { q max = max {q,k} k [,m ] (22) q last = q,m In fact, the feasblty of a hgh prorty task τ k s affected by the sze qj max of the longest subjob of each task τ j wth prorty P j < P k. Moreover, the length q last of the fnal subjob of τ drectly affects ts response tme. In fact, all hgher prorty jobs arrvng durng the executon of τ s fnal subjob do not cause a preempton, snce ther executon s postponed at the end of τ. Therefore, n ths model, each task wll be characterzed by the followng 5-tuple: {C,D,T,q max,q last }. For example, consder the same task set of Table I, and suppose that τ 2 s splt nto two subjobs of 2 and unt, and τ 3 s splt nto two subjobs of 4 and 2 unts. The schedule produced by Deadlne Monotonc wth such a splttng s feasble and t s llustrated n Fgure 6. τ τ 2 τ Fg. 6. Schedule produced by Deadlne Monotonc for the task set reported n Table I, when τ 2 s splt nto two subjobs of 2 and unt, and τ 3 s splt nto two subjobs of 4 and 2 unts, respectvely. A. Feasblty analyss Feasblty analyss for tasks wth fxed preempton ponts can be carred out n a very smlar way as the non-preemptve case, wth the followng dfferences: The blockng factor B to be consdered for each task τ s equal to the length of longest subjob (nstead of the longest task) among those wth lower prorty: B = max j:p j<p {q max j }. (23) The last non-preemptve chunk of τ s equal to q last (nstead of C ). The response tme analyss for a task τ has to consder all the jobs wthn the longest Level- Actve Perod, defned n Equaton (2). Ths means that the response tme of τ must be computed for all jobs τ,k wth k [,K ], where K s defned n Equaton (3). For a generc jobτ,k, the start tmes,k of the last subjob can be computed consderng the blockng tme B, the computaton tme of the precedng (k ) jobs, the subjobs of τ,k precedng the last one (C q last ), and the nterference of the tasks wth prorty hgher than P. Hence, s,k can be computed wth the followng recurrent relaton: s (0),k = B +C q last + C h h:p h >P s (l),k = B +kc q last + ( ) (l ) s (24),k + C h. h:p h >P Also n ths case, the orgnal result reported by Brl et al. [20] adopted a more complex expresson, separatng the lowest prorty task from the hgher prorty ones. The expresson presented here has been smplfed thanks to the nteger tme model, provded the blockng term s computed usng Equaton (23). Snce, once started, the last subjob cannot be preempted, the fnshng tme f,k can be computed as f,k = s,k +q last. (25) The response tme of task τ can then be computed usng Equaton (6), and the task set s feasble f and only f Condton (7) s satsfed. B. Longest non-preemptve nterval As done n Secton VI-B under deferred preemptons, t s nterestng to compute, also under task splttng, the longest non-preemptve nterval Q for each task τ that can guarantee the schedulablty. It s worth observng that splttng tasks nto subjobs allows achevng a larger Q, because a task τ cannot be preempted durng the executon of the last q last unts of tme. As shown by Bertogna et al. [3], there are cases n whch Q can be computed even when the task set s not preemptvely feasble, because the last non-preemptve regon allows reducng the nterference from hgher prorty tasks. Defnng β,k as the blockng tolerance of the k-th job of τ after a crtcal nstant, the schedulablty of such a job can be checked usng the followng condton [3]: t Π,k : B t kc +q last h:p h >P ( t where def Π,k = ( (k )T,(k )T +D q last ] ) + C h, {ht j, h N,j } { (k )T +D q last (26) Hence, the blockng tolerance β,k becomes { β,k = max t kc +q last ( } t + )C h. (27) t Π,k h:p h >P }.

8 8 The blockng tolerance of task τ can be computed as the mnmum blockng tolerance among the frst K jobs of τ n the longest Level- Actve Perod: β = mn β,k, (28) k [,K ] where K s defned n Equaton (3). From Equaton (27), t s easy to see that the blockng tolerances β,k do not depend on B, whch can be set to β, wthout affectng the analyss. The longest non-preemptve nterval Q that guarantees the feasblty for each task τ can then be computed by Theorem 2, usng the blockng tolerances gven by Equaton (28). As prevously mentoned, the maxmum length of the nonpreemptve chunk under fxed preempton ponts s larger than n the case of deferred preemptons. It s worth pontng out that the value of Q for task τ only depends on the β k of the hgher prorty tasks, as expressed n Equaton (20), and the blockng tolerance β s a functon of q last, as clear from Equaton (28). Note that when tasks are assumed to be preemptvely feasble, the analyss can be lmted to the frst job of each task. In ths case, the blockng tolerance β of task τ s: β = β,. (29) VIII. ASSESSMENT OF THE APPROACHES The lmted preempton methods presented n ths paper can be compared under several aspects, such as: mplementaton complexty, predctablty n estmatng the preempton cost, effectveness n mprovng schedulablty and n reducng the number of preemptons. A. Implementaton ssues The preempton threshold mechansm can be mplemented by rasng the executon prorty of the task, as soon as t starts runnng. The mechansm can be easly mplemented at the applcaton level by callng, at the begnnng of the task, a system call that ncreases the prorty of the task at ts threshold level. The mechansm can also be fully mplemented at the operatng system level, wthout modfyng the applcaton tasks. To do that, the kernel has to ncrease the prorty of a task at the level of ts threshold when the task s scheduled for the frst tme. In ths way, at ts frst actvaton, a task s nserted n the ready queue usng ts nomnal prorty. Then, when the task s scheduled for executon, ts prorty becomes equal to ts threshold, untl completon. Note that, f a task s preempted, ts prorty remans at ts threshold level. Note that preempton threshold schedulng s already used n the ThreadX real-tme operatng system by Express Logc Inc. and n the Erka Enterprse real tme kernel by Evdence, and t represents an example of a great success of transferrng research results to ndustral applcatons. In deferred preempton (floatng model), non-preemptve regons can be mplemented by proper kernel prmtves that dsable and enable preempton at the begnnng and at the end of the regon, respectvely. As an alternatve, preempton can be dsabled by ncreasng the prorty of the task at ts maxmum value, and can be enabled by restorng the nomnal task prorty. In the actvaton-trggered mode, non-preemptve regons can be realzed by settng a tmer to enforce the maxmum nterval n whch preempton s dsabled. Intally, all tasks start executng n non-preemptve mode. When τ s runnng and a task wth prorty hgher than P s actvated, a tmer s set by the kernel (nsde the actvaton prmtve) to nterrupt τ after q unts of tme. Untl then, τ contnues executng n non-preemptve mode. The nterrupt handler assocated to the tmer must then call the scheduler to allow the hgher prorty task to preempt τ. Notce that, once a tmer has been set, other addtonal actvatons before the tmeout wll not prolong the tmeout any further. Fnally, cooperatve schedulng does not need specal kernel support, but t requres the programmer to nsert n each preempton pont a prmtve that calls the scheduler, so enablng pendng hgh-prorty tasks to preempt the runnng task. As a last remark, note that the fxed preempton pont model can also be adopted to model electrcal loads of a dstrbuted smart grd, where power applances can be nterrupted only at pre-defned ponts [32]. B. Predctablty As observed n Secton I, the runtme overhead ntroduced by the preempton mechansm depends on the specfc pont where the preempton takes place. Therefore, a method that allows predctng where a task s gong to be preempted smplfes the estmaton of preempton costs, permttng a tghter estmaton of task WCETs. Unfortunately, under preempton thresholds, the specfc preempton ponts depend on the actual executon of the runnng task and on the arrval tme of hgh prorty tasks, hence t s practcally mpossble to predct the exact locaton where a task s gong to be preempted. Under deferred preemptons (floatng model), the poston of non-preemptve regons s not specfed n the model, thus they are consdered to be unknown. In the actvaton-trggered model, nstead, the tme at whch the runnng task wll be preempted s setq unts of tme after the arrval tme of a hgher prorty task. Hence, the preempton poston depends on the actual executon of the runnng task and on the arrval tme of the hgher prorty task. Therefore, t can hardly be predcted off-lne. On the contrary, under fxed preempton ponts, the locatons where preemptons may occur are explctly defned by the programmer at desgn tme, hence the correspondng overhead can be estmated more precsely by tmng analyss tools. For nstance, Bertogna et al. [33] presented an algorthm for selectng the preempton ponts that mnmze the overall preempton cost wthout compromsng the feasblty of the task set. C. Effectveness The effectveness of an algorthm that lmts preemptons can be evaluated ether n terms of schedulablty or by the number of preemptons. As long as schedulablty s concerned, all the lmted preemptve methods (under fxed prortes) domnate both fully preemptve schedulng and non-preemptve schedulng, even when preempton cost s neglected. Such a behavor has been clearly llustrated by showng how the sample task set n Table I cannot be scheduled by fully preemptve and non-preemptve Deadlne Monotonc, whereas t s schedulable usng any lmted preemptve algorthm. Ths property wll be

9 9 also evaluated by smulaton n the next secton, usng more quanttatve data. The number of preemptons each task can experence depends of dfferent parameters. Under preempton thresholds, a task τ can only be preempted by tasks wth prorty greater than ts threshold θ. Hence, f preempton cost s neglected, an upper bound ν on the number of preemptons τ can experence can be computed by countng the number of actvatons of tasks wth prorty hgher than θ occurrng n [0,R ] that s: ν = R. (30) h:p h >θ Ths s an upper bound because each hgher prorty arrval s counted as a dfferent preempton, even when multple arrvals cause a sngle preempton. Under deferred preempton, the number of preemptons occurrng on τ can be upper bounded usng the non-preemptve ntervalq specfed for the task. If preempton cost s neglected, we smply have: C ν =. q Ths s a pessmstc estmaton snce a task τ s assumed to be preempted after every nterval of length q, even n the absence of hgher prorty jobs. In ths case, a better upper bound can be derved from Equaton (30), by replacng θ wth P. Note that when preempton cost s not neglgble, the derved upper bounds are not applcable, snce task computaton tmes also depend on the number of preemptons, leadng to a crcular dependency, as shown by Yao et al. [34]. Under cooperatve schedulng, the number of preemptons can be easly upper bounded by the mnmum between the number of effectve preempton ponts nserted n the task code and the number of hgher prorty jobs actvated durng the response tme of the consdered task. IX. SIMULATION EXPERIMENTS Ths secton presents a set of smulaton results performed on randomly generated task sets, wth the objectve of evaluatng the effects of the dfferent schedulng approaches on the number of preemptons and the system schedulablty. Specfc tests have been carred out to evaluate how schedulablty s affected by the sze of non-preemptve regons and by the preempton cost. The aforementoned algorthms have been consdered n the comparson, all executed under the Deadlne Monotonc prorty assgnment. Each task set was generated as follows. The UUnFast [35] algorthm was used to generate a set of n perodc tasks wth total utlzaton equal to a desred value U. Then, for each task τ, ts computaton tme C was generated as a random nteger unformly dstrbuted n the nterval [00, 500], and ts perod T was computed as T = C /U. The relatve deadlne D was generated as a random nteger unformly dstrbuted n the range [C +α (T C ), T ], wth α = 0.5. To reduce preemptons as mush as possble, n the PTS algorthm, threshold prortes were set at the hghest possble value usng the method descrbed n Secton V-B. Smlarly, n both DPS and FPP, the length of non-preemptve regons was set at the hghest possble value to keep the task set feasble, usng the methods llustrated n Secton VI-B and Secton VII-B, respectvely. In the rest of ths secton, three sets of experments are presented: the frst set s amed at evaluatng how the number of preemptons s affected by dfferent parameters; the second set evaluates the schedulablty level n the deal case of zero perempton cost, whereas the thrd set compares the feasblty level n the presence of non-neglgble cost. A. Number of preemptons The frst set of experments was carred out to montor the total number of preemptons generated by the dfferent algorthms on a perodc task set wthn a smulaton wndow of unts of tme. In partcular, each value shown n the graphs plots the average over,000 runs. To make the comparson far, only preemptvely feasble task sets were consdered and the preempton cost was assumed to be zero. In ths set of experments, the non-preemptve schedulng algorthm (NPS) s not reported, snce the number of preemptons s always zero, for any utlzaton. Such a great performance of NPS, however, s compensated by a poor schedulablty level, whch s better evaluated n the second set of experments. The curve for deferred preempton schedulng (DPS) corresponds to the actvaton-trggered model. We dd not nclude the floatng model because n ths model no nformaton s provded on the mnmum length and poston of the non-preemptve regons. The number of preemptons s therefore the same as n the fully preemptve case (FPS). Fgure 7 shows how the performance of the varous algorthms vares as a functon of the task set utlzaton, for task sets composed of n = 0 tasks. As clear from the graphs, the use of non-preemptve regons, ether fxed (FPP) or not (DPS), allows achevng a hgher reducton wth respect to preempton thresholds, especally for task set utlzatons greater than 70%. Note that n all the graphs related to ths experment, DPS performs slghtly better than FPP. Ths can be explaned consderng that, when preempton ponts are fxed, hgh prorty jobs arrvng slghtly before and after a preempton pont generate two dstnct preemptons (although deferred), whereas under DPS the frst arrval always trggers a non-preemptve nterval of length Q, whch prevents other subsequent arrvals to generate addtonal preemptons. In most practcal cases, however, such a performance dfference s qute neglgble, hence FPP s stll to be preferred aganst DPS for the reasons expressed n the prevous sectons. Fgure 8 shows the average number of preemptons as a functon of the number of tasks, when U = 0.9. Note that preemptons rapdly decrease wth n for all the algorthms. Ths s due to the fact that, for a gven utlzaton, large task sets are characterzed by tasks wth smaller computaton tmes, whch have less chance to be preempted. For task sets wth n < 20, however, both FPP and DPS lead to a sgnfcant reducton wth respect to PTS. B. Schedulablty wth zero preempton cost The second set of experments was carred out to test the mpact of the varous algorthms on the task set schedulablty, whch has been verfed usng the feasblty tests reported n ths paper, assumng zero preempton cost. The performance of

10 0 Average Number of Preemptons 4 x FPS PTS FPP DPS Rato of Feasble task sets EDF FPP PTS FPS NPS Total Utlzaton Fg. 7. Average number of preemptons versus utlzaton when n = Total Utlzaton Fg. 9. Feasble rato versus utlzaton when n = 0. Average Number of Preemptons 0 x FPS PTS FPP DPS Rato of Feasble task sets EDF FPP PTS FPS NPS Number of Tasks Fg. 8. Average number of preemptons versus number of tasks when U = Number of Tasks Fg. 0. Feasble rato as a functon of n, when U = 0.9. the algorthms was evaluated by comparng the feasble rato, calculated as the number of feasble task sets dvded by the total number of generated sets. In each experment, task sets were randomly generated for each parameter confguraton. The assumpton on preemptve feasblty was removed and the percentage of feasble task sets was montored as a functon of dfferent parameters. In ths set of experments, DPS s not shown, snce ts performance s the same as FPS, as mentoned n Secton VI-A. On the other hand, fully preemptve Earlest Deadlne Frst (EDF) [9] has been ncluded n the graphs to evaluate the dfference wth respect to an optmal soluton. Fgure 9 shows the performance of the varous algorthms as a functon of the task set utlzaton, when n = 0. It s worth observng that both FPP and PTS mprove the schedulablty level wth respect to FPS, but FPP s able to acheve a larger mprovement, especally for hgher utlzatons (U > 0.85). For example, FPP s able to schedule 30% more task sets than FPS for U around 0.9. A second experment has been carred out to test how schedulablty s affected by the number of tasks. Here, the total system utlzaton was set to U = 0.9 and the number of tasks was vared from 4 to 40. The results are reported n Fgure 0. Note that FPP always outperforms all the other fxed prorty algorthms, although the mprovement decreases for larger task sets. Ths can be explaned observng that a large task set s more lkely to have smaller blockng tolerances, due to the hgher number of generated deadlnes. Ths phenomenon lmts the length of non-preemptve regons of lower prorty tasks, hence FPP has less chance to mprove schedulablty for large task sets. On the other hand, the performance of NPS ncreases wth n, because larger task sets tend to have smaller computaton tmes, whch ntroduce smaller blockng tmes n hgher prorty tasks. C. Schedulablty wth preempton cost Consderng that FPP s the algorthm that exhbts the best performance wth respect to the other fxed prorty schemes, a fnal experment was carred out to evaluate how the feasblty rato of FPP s affected by the preempton cost. In ths case, however, exstng feasblty tests that take preempton costs nto account are qute pessmstc, snce they count a preempton for each hgh prorty job arrval. For ths reason, n ths set of experments, an approxmated feasblty rato was computed by smulaton, consderng a task set schedulable f no deadlne mss occurred durng the entre smulaton nterval. Even f such a smulaton represents just a necessary condton for feasblty, t allows gvng a rough estmaton of the schedulablty performance when preempton cost s taken nto account. Preempton cost has been ncorporated nto response tme analyss by Altmeyer et al. [36] to obtan tght bounds on feasblty. However, the approach requres detaled nformaton on the task structure and cache usage, whch s not n the scope of ths paper. In the experment, the length q of the non-preemptve regons n each task was vared from 0 to C max, (.e., the longest

11 computaton tme among the tasks), through a parameter λ varyng n [0,], such that q = λc max. In ths way, FPS and NPS result to be two specal cases of FPP, obtaned wth λ = 0 and λ =, respectvely. Note that, f q C, task τ s entrely executed n non-preemptve mode. The same q value s used for all tasks n the system n order to vary the length of the non-preemptve regons n a unform way for the whole task set. However, a much better schedulablty performance could be obtaned adoptng a dfferent q value for each task τ, as explaned n Secton VII. The preempton cost, denoted by γ, was assumed to be a fxed value for each task. Fgure shows the feasblty rato acheved by FPP as a functon of the task set utlzaton, for dfferent values of λ n [0,]. Here, the task set has n = 0 tasks and the preempton cost s γ = 30. Note that dfferent curves ntersect each other, meanng that the relatve performance depends on the task set utlzaton. In partcular, usng smaller non-preemptve regons s more effcent for small task set utlzatons, when there are less preemptons due to the reduced workload. On the other hand, when the total utlzaton ncreases, havng longer non-preemptve regons mght help reducng the number of preemptons, reducng the overhead experenced. In the consdered confguraton, the curve for λ = 0.2 (.e., for q = C max 0.2 = 00) has the best performance untl U = 0.8, whle the curve for λ = 0.4 (.e., for q = C max 0.4 = 200) has a better performance for larger utlzatons. It s nterestng to note that the curve for fully preemptve schedulng (λ = 0) has a rapd performance degradaton, beng the hghest one for U < 0.7 and the lowest one when U > Fnally, Fgure 2 shows how the overall system feasblty, computed for all the task sets generated wthn the utlzaton range [0.05, 0.95], vares as a functon of λ, from the fully preemptve case (λ = 0), to the non-preemptve case (λ = ). Dfferent curves are plotted for dfferent preempton costs rangng from 0 to 50 unts of tme, wth a step of 0. It s worth notng that the hghest feasblty rato s not acheved under fully preemptve schedulng (λ = 0), even for low preempton costs. Also note that ncreasng the preempton cost the hghest feasblty rato s acheved for longer non-preemptve regons (hgher λ). Ths confrms that lmted preemptve schedulng domnates fully preemptve and non-preemptve schedulng, even when preempton cost s neglgble, and becomes more effectve for larger preempton costs. Also note that, when λ ncreases, each task has less chances to be preempted, hence the cost s less relevant and the gap between lnes reduces. Eventually, all lnes merge at one pont, snce NPS does suffer from the preempton cost. X. CONCLUSIONS Ths paper presented a survey of lmted preemptve schedulng algorthms, as methods for ncreasng the predctablty and effcency of real-tme systems. The most relevant result that clearly emerges from the experments s that, under fxed prorty schedulng, any of the consdered algorthms domnates both fully preemptve and non-preemptve schedulng, even when preempton cost s neglected. As dscussed n the prevous sectons, each specfc algorthm for lmtng preemptons has advantages and dsadvantages. The Rato of Feasble Task Sets λ = 0 (FPS) λ = 0.2 λ = 0.4 λ = 0.6 λ = 0.8 λ = (NPS) Total Utlzaton Fg.. Feasble rato versus utlzaton under dfferent q values, wth n = 0 and γ = 30. Rato of All Feasble Task Sets wth Utlzaton n [0.05, 0.95] Fg γ = 0 γ = 0 γ = 20 γ = 30 γ = 40 γ = λ (Rato of q over C ) max Overall feasble rato versus length of non-preemptve regons. preempton threshold mechansm has a smple and ntutve nterface and can be mplemented by ntroducng a low runtme overhead; however, preempton cost cannot be easly estmated, snce the poston of each preempton, as well as the overall number of preemptons for each task, cannot be determned offlne. Usng deferred preemptons, the number of preemptons for each task can be better estmated, but stll the poston of each preempton cannot be determned off-lne. Fxed preempton ponts represents the most predctable soluton for estmatng preempton costs, snce both the number of preemptons and ther postons are fxed and known from the task code. Moreover, smulaton experments clearly show that the FPP algorthm s the one generatng less preemptons and hgher schedulablty ratos for any task set parameter confguratons. However, FPP requres addng explct preempton ponts n the program, hence achevng portablty of legacy code s stll a challenge for future works. REFERENCES [] M. Grener and N. Navet, Fne-tunng MAC-level protocols for optmzed real-tme qos, IEEE Transactons on Industral Informatcs, vol. 4, no., pp. 6 5, February [2] C.-G. Lee, J. Hahn, Y.-M. Seo, S. L. Mn, R. Ha, S. Hong, C. Y. Park, M. Lee, and C. S. Km, Analyss of cache-related preempton delay n fxed-prorty preemptve schedulng, IEEE Transactons on Computers, vol. 47, no. 6, pp , 998. [3] H. Ramaprasad and F. Mueller, Tghtenng the bounds on feasble preempton ponts, n Proceedngs of the 27th IEEE Real-Tme Systems Symposum (RTSS 2006), Ro de Janero, Brazl, December 5-8, 2006.

12 2 [4], Boundng worst-case response tme for tasks wth non-preemptve regons, n Proceedngs of the Real-Tme and Embedded Technology and Applcatons Symposum (RTAS 2008), St. Lous, Mssour, USA, Aprl 22-24, [5], Tghtenng the bounds on feasble preemptons, ACM Transactons on Embedded Computng Systems, vol. 0, no. 2, pp. 34, December 200. [6] L. Sha, R. Rajkumar, and J. Lehoczky, Prorty nhertance protocols: An approach to real-tme synchronzaton, IEEE Transactons on Computers, vol. 39, no. 9, pp , September 990. [7] T. P. Baker, Stack-based schedulng for realtme processes, Real-Tme Systems, vol. 3, no., pp , Aprl 99. [8] G. Buttazzo and A. Cervn, Comparatve assessment and evaluaton of jtter control methods, n Proceedngs of the 5th Internatonal Conference on Real-Tme and Network Systems (RTNS 07), Nancy, France, March 29-30, [9] P. Ga, L. Aben, M. Gorg, and G. Buttazzo, A new kernel approach for modular real-tme systems development, n Proceedngs of the 3th IEEE Euromcro Conference on Real-Tme Systems (ECRTS 200), Delft, The Netherlands, June 3-5, 200. [0] R. Marau, P. Lete, M. Velasco, P. Mart, L. Almeda, P. Pedreras, and J. Fuertes, Performng flexble control on low-cost mcrocontrollers usng a mnmal real-tme kernel, Industral Informatcs, IEEE Transactons on, vol. 4, no. 2, pp , May [] B. D. Bu, M. Caccamo, L. Sha, and J. Martnez, Impact of cache parttonng on mult-taskng real tme embedded systems, n IEEE Proceedngs of the 4th Int. Conf. on Embedded and Real-Tme Computng Systems and Applcatons (RTCSA 2008), Kaohsung, Tawan, August 25-27, [2] S. Altmeyer and G. Gebhard, WCET analyss for preemptve schedulng, n Proc. of the 8th Int. Workshop on Worst-Case Executon Tme (WCET) Analyss, Prague, Czech Republc, July 2008, pp [3] G. Gebhard and S. Altmeyer, Optmal task placement to mprove cache performance, n Proc. of the 7th ACM-IEEE Int. Conf. on Embedded Software (EMSOFT 07), Salzburg, Austra, October -3, [4] C. L, C. Dng, and K. Shen, Quantfyng the cost of context swtch, n Proc. of ACM Workshop on Expermental Computer Scence (ExpCS 07), San Dego, Calforna, June 3-4, [5] Y. Wang and M. Saksena, Schedulng fxed-prorty tasks wth preempton threshold, n Proc. of the 6th IEEE Int. Conference on Real-Tme Computng Systems and Applcatons (RTCSA 99), Hong Kong, Chna, December 3-5, 999. [6] S. Baruah, The lmted-preempton unprocessor schedulng of sporadc task systems, n Proc. of the 7th Euromcro Conf. on Real-Tme Systems (ECRTS 05), Palma de Mallorca, Balearc Islands, Span, July 6-8, 2005, pp [7] A. Burns, Preemptve prorty based schedulng: An approprate engneerng approach, S. Son, edtor, Advances n Real-Tme Systems, pp , 994. [8] R. J. Brl, J. J. Lukken, and W. F. J. Verhaegh, Worst-case response tme analyss of real-tme tasks under fxed-prorty schedulng wth deferred preempton revsted, n Proc. of the 9th Euromcro Conf. on Real-Tme Systems (ECRTS 07), Psa, Italy, July 4-6, 2007, pp [9] C. Lu and J. Layland, Schedulng algorthms for multprogrammng n a hard-real-tme envronment, Journal of the Assocaton for Computng Machnery, vol. 20, no., pp. 46 6, January 973. [20] R. Brl, J. Lukken, and W. Verhaegh, Worst-case response tme analyss of real-tme tasks under fxed-prorty schedulng wth deferred preempton, Real-Tme System, vol. 42, no. -3, pp. 63 9, [2] J. Leung and J. Whtehead, On the complexty of fxed-prorty schedulng of perodc real-tme tasks, Performance Evaluaton, vol. 2, no. 4, pp , 982. [22] R. I. Davs, A. Burns, R. J. Brl, and J. J. Lukken, Controller area network (CAN) schedulablty analyss: Refuted, revsted and revsed, Real-Tme System, vol. 35, no. 3, pp , [23] G. Yao, G. Buttazzo, and M. Bertogna, Feasblty analyss under fxed prorty schedulng wth fxed preempton ponts, n Proc. of the 6th IEEE Int. Conf. on Embedded and Real-Tme Computng Systems and Applcatons (RTCSA 200), Macau, Chna, August 23-25, 200. [24] U. Keskn, R. Brl, and J. Lukken, Exact response-tme analyss for fxed-prorty preempton-threshold schedulng, n Work-n-Progress Sesson of the 5th Int. Conf on Emergng Technologes and Factory Automaton (ETFA 200), Blbao, Span, September 3-6, 200. [25] J. Regehr, Schedulng tasks wth mxed preempton relatons for robustness to tmng faults, n Proc. of the 23rd IEEE Real-Tme Systems Symposum (RTSS 2002), Austn, Texas, USA, December 3-5, [26] M. Saksena and Y. Wang, Scalable real-tme system desgn usng preempton thresholds, n Proc. of the 2st IEEE Real-Tme Systems Symposum (RTSS 00), Orlando, Florda, USA, November 27-30, [27] M. Bertogna and S. Baruah, Lmted preempton EDF schedulng of sporadc task systems, IEEE Transactons on Industral Informatcs, vol. 6, no. 4, pp , 200. [28] M. Short, Improved schedulablty analyss of mplct deadlne tasks under lmted preempton edf schedulng, n Proceedngs of the 6th IEEE Conference on Emergng Technologes and Factory Automaton (ETFA 20), September 20, pp. 8. [29] G. Yao, G. Buttazzo, and M. Bertogna, Boundng the maxmum length of non-preemptve regons under fxed prorty schedulng, n Proc. of the 5th IEEE Int. Conf. on Embedded and Real-Tme Computng Systems and Applcatons (RTCSA 2009), Bejng, Chna, August 24-26, [30] E. Bn and G. C. Buttazzo, Schedulablty analyss of perodc fxed prorty systems, IEEE Transactons on Computers, vol. 53, no., pp , [3] M. Bertogna, G. Buttazzo, and G. Yao., Improvng feasblty of fxed prorty tasks usng non-preemptve regons, n Proceedngs of 32nd IEEE Real-Tme Systems Symposum (RTSS 20), Venna, Austra, Nov Dec. 2, 20. [32] T. Facchnett and M. D. Vedova, Real-tme modelng for drect load control n cyber-physcal power systems, IEEE Transactons on Industral Informatcs, vol. 7, no. 4, pp , 20. [33] M. Bertogna, O. Xhan, M. Marnon, F. Esposto, and G. Buttazzo, Optmal selecton of preempton ponts to mnmze preempton overhead, n Proc. of the 23rd Euromcro Conf. on Real-Tme Systems (ECRTS ), Porto, Portugal, July 6-8, 20. [34] G. Yao, G. Buttazzo, and M. Bertogna, Comparatve evaluaton of lmted preemptve methods, n Proc. of the 5th IEEE Int. Conf. on Emergng Techonologes and Factory Automaton (ETFA 200), Blbao, Span, September 3-6, 200. [35] E. Bn and G. C. Buttazzo, Measurng the performance of schedulablty tests, Real-Tme Systems, vol. 30, no. -2, pp , [36] S. Altmeyer, R. Davs, and C. Maza, Cache related pre-empton delay aware response tme analyss for fxed prorty pre-emptve systems, n Proceedngs of 32nd IEEE Real-Tme Systems Symposum (RTSS 20), Venna, Austra, Nov Dec. 2, 20. Gorgo C. Buttazzo s Full Professor of Computer Engneerng at the Scuola Superore Sant Anna of Psa. He graduated n Electronc Engneerng at the Unversty of Psa n 985, receved a Master n Computer Scence at the Unversty of Pennsylvana n 987, and a Ph.D. n Computer Engneerng at the Scuola Superore Sant Anna of Psa n 99. From 987 to 988, he worked on actve percepton and real-tme control at the G.R.A.S.P. Laboratory of the Unversty of Pennsylvana, Phladelpha. Prof. Buttazzo has been Program Char and General Char of the major nternatonal conferences on real-tme systems. He s Edtor n Chef of Real-Tme Systems (Sprnger), Assocate Edtor of the IEEE Transactons on Industral Informatcs and Char of the IEEE Techncal Commttee on Real-Tme Systems. He has authored 6 books on real-tme systems and over 200 papers n the feld of real-tme systems, schedulng algorthms, overload management, robotcs, and neural networks. Marko Bertogna s Assstant Professor at Unversty of Modena and Reggo Emla, Italy. Before, he held the same poston at the Scuola Superore SantAnna of Psa, Italy, where he also receved a Ph.D. n Computer Engneerng n He graduated (summa cum laude) n Telecommuncatons Engneerng at the Unversty of Bologna n In 2006, he vsted the Unversty of North Carolna at Chapel Hll, workng wth prof. Sanjoy Baruah on schedulng algorthms for sngle and multcore real-tme systems. Hs research nterests nclude schedulng and schedulablty analyss of real-tme multprocessor systems, protocols for the exclusve access to shared resources, resource reservaton algorthms and reconfgurable devces. He has authored over 30 papers n nternatonal conferences and journals n the feld of real-tme systems, recevng four Best Paper Awards. He s Senor Member of IEEE.

13 Gang Yao s a Postdoctoral Research Collaborator at the Unversty of Illnos at Urbana Champagn. He receved a Ph.D. n Computer Engneerng from the Scuola Superore SantAnna of Psa, Italy, n 200. He receved the BE and ME degrees from Tsnghua Unversty, Bejng, Chna. Hs nterests nclude realtme schedulng algorthms, safety-crtcal systems and shared resource protocols. 3