Perfecting Preemption Threshold Scheduling for Object-Oriented Real-Time System Design: From The Perspective of Real-Time Synchronization

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1 Perfectng Preempton Threshold Schedulng for Obect-Orented Real-Tme System Desgn: From The Perspectve of Real-Tme Synchronzaton Saehwa Km School of Electrcal Engneerng and Computer Scence Seoul Natonal Unversty Seoul 5-74 Korea Seongsoo Hong School of Electrcal Engneerng and Computer Scence Seoul Natonal Unversty Seoul 5-74 Korea Tae-Hyung Km Dept. of Computer Scence and Engneerng Hanyang Unversty Ansan Kyungg-Do Korea ABSTRACT In spte of the prolferaton of obect-orented desgn methodologes n contemporary software development ther applcaton to real-tme embedded systems has been lmted because of the practtoner s conservatve atttude toward handlng tmng constrants. In fact ths conservatve atttude s well-grounded because tradtonal prorty-based schedulng technques cannot be straghtforwardly ntegrated nto them. The automated mplementaton from the obect-orented real-tme desgns usually ncurs a large number of tasks whch under tradtonal prorty-based schedulng technques does not scale well due to excessve preempton overheads. Recently preempton threshold schedulng was ntroduced to reduce runtme mult-taskng overhead whle mprovng schedulablty by explotng non-preemptblty as much as possble. Unfortunately the preempton threshold schedulng cannot be drectly adopted nto the obect-orented desgn methods due to the lack of realtme synchronzaton. In ths paper we present the essental bass of real-tme synchronzaton for preempton threshold schedulng. Specfcally we ntegrate the prorty nhertance protocol the prorty celng protocol and the mmedate nhertance protocol nto preempton threshold schedulng. We also provde ther schedulablty analyses. Consequently the ntegrated scheme whch mnmzes worst-case context swtches s approprate for the automated mplementaton of real-tme obect-orented desgn models Categores and Subect Descrptors D.4. [Operatng Systems]: Process anagement schedulng. General Terms Theory Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse or republsh to post on servers or to redstrbute to lsts requres pror specfc permsson and/or a fee. CTES 0 SCOPES 0 June 9-00 Berln Germany. Copyrght 00 AC /0/0006 $5.00. Keywords Preempton threshold schedulng real-tme synchronzaton prorty nhertance protocols prorty celng protocol obectorented real-tme system desgn.. INTRODUCTION Developng a real-tme embedded system s a sophstcated task. The monolthc approach to developng large and/or complex computer systems s comng to an end n the era of contemporary software development. Nonetheless ntrnsc dffcultes arsng from tmng constrants n the real-tme embedded applcatons stll te up practtoners wth a rather conservatve approach to developng embedded systems. any early real-tme system researchers have attached mportance to tmng analyss at desgn tme n order to derve a set of feasble tasks [ 3 4]. Ths has been qute successful and real-tme programmers are able to safely and relably derve a feasble set of tasks n advance. However as real-tme embedded systems get complex and sophstcated to meet the ncreased degree of safety relablty and performance requrements t becomes nevtable for real-tme system desgners to rely on systematc software desgn methodologes durng system development. Among a wde varety of software desgn methodologes obect-orented desgn methodologes have become domnant and popular snce they allow for easy software mantenance software reuse and component-based codng of complex real-tme systems that may evolve over tme. A recent trend n embedded systems development even tres to ht the lnes of hardware by harnessng software to mplement physcal layer functons n pursut of ts apparent advantages: re-usablty of hardware resources ease of upgrades flexblty to buld a dual- or multple-standards mplementaton and so on. Software defned rado (SDR s one of those representatve approaches. To cope wth the addtonal complexty the obect-orented desgn methodology should be seamlessly ntegrated nto tradtonal real-tme schedulablty analyss technques so that embedded system programmers can be equpped wth systematc software desgn methodologes and CASE tools as well. Tradtonal preemptve fxed prorty schedulng cannot be drectly used n ths ntegraton largely owng to ts excessve run-

2 tme overhead. Preempton threshold schedulng (PTS mproves both run-tme overhead and schedulablty but stll cannot be drectly used to ths end ether snce real-tme synchronzaton problems reman unsolved. In ths paper we present an essental bass for ther ntegraton by perfectng preempton threshold schedulng [ ] for real-tme synchronzaton.. Background Two prmary thrusts n embedded systems research are how to enhance schedulablty by devsng elaborate schedulng technques and how to ntegrate schedulablty analyss technques nto modern software engneerng desgn and mplementaton methodologes. Successfully appled schedulng technques have been based on preemptve fxed prorty schedulng n most real-tme systems developments snce u and ayland ntroduced t n ther poneerng paper []. However dynamc prorty schedulers can acheve hgher schedulablty than fxed ones and non-preemptve schedulers ncur less runtme overhead. Ths means that n fne-gran or medum-gran thread-based processng whch s the case especally n multthreaded mplementatons from real-tme obect-orented desgns the context swtchng overhead may overshadow the benefts of mult-threadng and preemptve schedulng. To allevate the run-tme overhead problem whle mprovng schedulablty ame at Express ogc Inc. ntroduced the noton of preempton threshold []. The preempton threshold regulates the degree of preemptveness n fxed-prorty schedulng. If the threshold of each task s the same as ts orgnal prorty then t s equvalent to the preemptve fxed prorty schedulng. If each task has the hghest threshold value n a system then t becomes a non-preemptve schedulng. As Wang and Saksena llustrated n [ ] the schedulablty of a task set under preemptve schedulng does not mply that the task set s also schedulable under non-preemptve schedulng and vce versa. Thus the preempton threshold schedulng s a good complement to preemptve fxed-prorty schedulng. It mproves schedulablty wthholds unnecessary preemptons reduces the number of tasks snce a group of non-preemptve tasks can be regarded as a unt and eventually helps allow for scalable real-tme system desgn. In the meantme there have been several research actvtes to ntegrate schedulablty analyss technques nto obect-orented desgn methodologes [5 6] based on the ROO (Real-tme Obect Orented odelng methodology [8]. The ntegraton s to provde many other advantages of obect-orented desgn methods and software engneerng tools for the automated mplementaton of real-tme embedded control systems from ROO-based desgn models. The most dffcult part of ths ntegraton s how to automatcally produce a thread-based mplementaton from a real-tme obect model wth tmng constrants. Saksena et al. ntate such a method usng one-toone mappng between obects and tasks for schedulablty [5] and mprove the performance usng preempton threshold schedulng to reduce the adverse effects of context swtchng n an automated mplementaton [].. Approaches and Contrbutons A real-tme system can be vewed as a collecton of concurrent obects that cooperate wth each other. Each obect may partcpate n multple system functons and as a result s subect to multple tmng constrants. In ths sense there are two extremes n mappng between obects and tasks. One s to map all obects nto a sngle task as n RoseRT for U-RT [9] and ObecTme for ROO [8]. Although ths s a practcal approach to reduce bng tme due to prorty nverson the system cannot be analyzed by the fxed-prorty schedulng theory. The alternatve s to map each obect nto a sngle task n order to perform tmng analyss wthn the obect-orented desgn technques as n [5]. Snce mult-taskng n ths mult-threaded mplementaton s expensve the preempton threshold schedulng s adopted n []. In our prevous work we presented a systematc schedulabltyaware method that can generate a mult-threaded mplementaton from a gven real-tme obect-orented desgn model [3 4]. Unlke the above mentoned approaches the mappng relatonshp between obects and tasks s not based to many-to-one or one-toone n our approach. Tasks are rather automatcally dentfed from a set of obects. Our method s a three-step process: ( dervng scenaros (end-to-end computaton unts ( dentfyng logcal threads and then (3 dervng physcal threads. ogcal threads are mapped from mutually exclusve scenaros and assgned prortes and preempton thresholds that guarantee schedulablty. To reduce the number of tasks those logcal threads are parttoned nto a mutually exclusve group of nonpreemptve ones. A group of non-preemptve logcal threads s n fact a physcal thread. Snce our approach s prmarly based upon real-tme synchronzaton under the preempton threshold schedulng t needs to be addressed n a comprehensve manner. Note that an obect-orented desgn produces a number of obect s for consstency of obect states and for mantenance of the run-tocompleton semantcs of a fnte state machne nsde each obect. Unfortunately real-tme synchronzaton under the preempton threshold schedulng has not been consdered yet. In ths paper we consder the problem of ntegratng three real-tme synchronzaton schemes nto the preempton threshold schedulng: they are the basc prorty nhertance protocol (BPI [5] the prorty celng protocol (PCP [5] and the mmedate prorty nhertance protocol (IIP [9]. In dong so we ntroduce the noton of effectve prorty nhertance and defne prorty celng and preempton threshold celng for reducng run-tme overhead. We also nvestgate ther schedulablty analyses. The remander of the paper s organzed as follows. Secton descrbes the task model wth proper defntons for the dscusson. In Secton 3 we dentfy the prorty nverson problem under PTS and present the revsed BPI protocol under PTS. In Sectons 4 and 5 we present the propertes of PCP and IIP under PTS and the schedulablty analyses of the proposed protocols respectvely. We conclude ths paper n Secton 6.. TASK ODE The task model used here s very smlar to that used n [ 5]. We assume a unprocessor envronment and allow only properly nested mutexes. We further assume a system wth a fxed set of tasks each of whch has a fxed perod known worst-case executon tme fxed prorty and preempton threshold. We denote a hgher prorty wth a larger value snce ths befts the ntutve meanng of beng a hgher threshold. The notatons and

3 ther descrptons used throughout the paper are summarzed n Table. Table. Summary of notatons for the task model. Notaton τ T C π γ p ϕ( Ψ Φ ξ z k β B S F R Descrpton A task The perod of task τ The worst-case executon tme of task τ The fxed-prorty of task τ The preempton threshold of task τ The effectve prorty of task τ A mutex (bnary semaphore Indvsble and operaton of mutex The celng of mutex The set of tasks that may use mutex The set of mutexes that task τ may use The set of mutexes that are currently ed by task τ The duraton of crtcal secton of task τ guarded by mutex k The bng tme of task τ due to synchronzaton The PTS bng tme of task τ The start tme of task τ The fnsh tme of task τ The response tme of task τ Under PTS each task has a preempton threshold n addton to ts regular prorty. Note that t s meanngful to assgn a task a preempton threshold that s no less than ts regular prorty snce a preempton threshold s used as an effectve run-tme prorty to control unnecessary preemptons. Snce the effectve prorty of a task s changed at run-tme due to prorty nhertance and task dspatchng under PTS t s desrable to precsely defne t. Conceptually the effectve prorty of a task s the prorty that s used by the kernel scheduler for selectng a task to be dspatched. Under PTS effectve prortes vary accordng to task states. We τ τ ={ ={ τ ={ ={ γ γ π π π π defne t n an operatonal manner as below. Effectve prorty p of τ = π f τ s released n ts perod and not yet dspatched; otherwse max(γ p p p such that τ τ τ are tasks bed by τ. In tradtonal prorty-based preemptve schedulng tasks may experence bng due to synchronzaton. Under PTS tasks may encounter another type of bng whch we name PTS bng. Task τ s sad to be n PTS bng f t s bed by a lower prorty task whose preempton threshold s hgher than π. We denote the duraton of PTS bng by B whle the duraton of other types of bng by β. 3. PREVENTING THE PRIORITY INVERSION PROBE Wthout usng prorty nhertance protocols catastrophc prorty nverson problems cannot be rectfed n a real-tme system that uses synchronzaton prmtves. The basc prorty nhertance protocol (BPI prevents preemptons that eventually cause prorty nverson. In ths secton we dentfy the prorty nverson problem under PTS formulate the BPI protocol under PTS and then descrbe ts propertes. 3. Prorty Inverson Problem under PTS The prorty nverson problem n tradtonal prorty-based schedulng occurs when a medum prorty task preempts a lower prorty task that bs a hgher prorty task. Under PTS we reformulate the orgnal problem nto the effectve prorty nverson problem by substtutng a prorty of a task wth ts effectve prorty. The ratonale behnd ths formulaton s obvous snce an effectve prorty takes the place of a prorty under PTS. In ths formulaton gven that task τ s bed by prorty nverson occurs ( when a medum prorty task wth γ π π preempts ; or ( when another task wth π π H γ preempts. These cases are llustrated n Fgure (a and (b τ τ ={ ={ τ ={ ={ γ γ π π π H π H γ γ τ preempt (attempt to bed by uncontrolled prorty nverson preempt preempt τ (attempt to bed by preempt uncontrolled prorty nverson t 0 t t t 3 t 4 (a Case. t 0 t t t 3 t 4 (b Case. Fgure. Prorty nverson problem under PTS.

4 respectvely. τ arrve (attempt to bed by τ preempt τ τ ={ ={ τ ={ ={ γ γ π π π π π H π γ H γ nhert γ drect bng arrve t 0 t t t 3 t 4 t 5 push-through bng t 6 push-through bng Fgure. Preventon of prorty nverson by BPI under PTS. 3. BPI under PTS We defne the BPI protocol under PTS usng effectve prortes as below. Protocol : BPI under PTS. Inhertance of effectve prortes. When task s bed by task wth π H > γ task nherts p H from task. Recovery of effectve prortes. When task exts from a crtcal secton task recovers p that t had before enterng that crtcal secton. We can easly see that ths defnton of BPI prevents preemptons that eventually cause prorty nverson. Fgure shows an example that follows Protocol. Snce nether does nor preempt τ prorty nverson s avoded. 3.3 Propertes of BPI under PTS BPI under PTS bears smlar propertes wth the orgnal BPI n [5]. In the orgnal protocol a task can be bed n one of three forms of bng: ( drect bng ( push-through bng and (3 transtve bng. In our protocol a task can be bed addtonally n PTS bng. Drect bng occurs when a hgher prorty task attempts to a mutex ed by a lower prorty task. It s to ensure the consstency of a non-preemptble shared resource. Push-through bng occurs under PTS when a medum prorty task attempts to preempt a lower prorty task that s bng a hgher prorty task as descrbed below. Push-through bng under PTS. Consder three tasks wth γ π γ π H and π γ H. If task s bed by task that already bed ths stuaton s referred to as push-through bng under PTS. In the above defnton task falls nto push-through bng snce the effectve prorty of task s greater than that of due to effectve prorty nhertance. Push-through bng s ntroduced to prevent preemptons that cause prorty nverson. In Fgure tasks and are bed n push-through bng durng the perod of (t 4 t 5 and (t 5 t 6 respectvely. Fnally transtve bng occurs when task s bed by whch n turn s bed by another task. Fgure 3 (a shows an example for transtve bng. Durng the perod of (t 6 t 7 s bed by whle bng. Therefore s ndrectly bed by n a transtve manner. As such transtve bng occurs when mutexes are accessed n a nested fashon. Addtonally a task can encounter chaned bng. Chaned ={ ={ P( V( ={ ={ P( V( ={ ={ γ π γ γ π π γ H π H (attempt to bed by transtve bng preempt preempt (attempt to bed by drect bng preempt (attempt to bed by celng bng t 0 t t t 3 t 4 t 5 t 6 t 7 t 8 (a t 8 t 0 t t t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 0 t t t 3 (b Fgure 3. (a Transtve bng n BPI (b transtve bng preventon n PCP.

5 ={ ={ P( V( ={ ={ P( V( ={ ={ γ π γ γ π π γ H π H (attempt to bed by (attempt to bed by (attempt to bed by preempt preempt (attempt to bed by celng bng t 0 t t t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 0 t 0 t t t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 0 t t t 3 (a Fgure 4. (a Chaned bng n BPI (b chaned bng preventon n PCP. (b bng (or a chan of bng s sad to occur f a task s repeatedly bed when t enters ts crtcal sectons. An example for chaned bng s llustrated n Fgure 4 (a where task s bed durng the perod of (t 6 t 7 and bed agan durng (t 9 t 0. Note that chaned bng s not a form of bng but refers to a stuaton where a task s bed more than once. Note that the BPI protocol alone does not prevent dead. Dead may occur when multple tasks try to access nested mutexes n a crcular manner. Fgure 5 shows an example for dead. In ths example both tasks and need to acqure two mutexes and. As shown wats for to release and wats for to release smultaneously whle and are holdng and respectvely. Therefore a dead occurs at tme t PREVENTING DEADOCK TRANSITIVE BOCKING AND CHAINED BOCKING Although BPI prevents prorty nverson by means of pushthrough bng t may ncur dead and excessvely long bng delay due to transtve and chaned bng as dscussed n Secton 3.3. The prorty celng protocol (PCP was ntroduced to solve these problems [5]. In ths secton we defne two versons of PCP under PTS: one wth prorty celngs and the other wth preempton threshold celngs. We refer to the former as PC-PCP and the latter as PTC-PCP. Then we nvestgate ther propertes compare them and present schedulablty analyss. ={ ={ P( V( ={ ={ P( V( γ π γ H π H preempt (attempt to bed by (attempt to bed by preempt (try to bed by celng bng dead t 0 t t t 3 t 4 t 5 (a t 0 t t t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 0 t (b Fgure 5. (a Dead n BPI (b dead preventon n PCP.

6 4. PCP under PTS wth Prorty Celngs The underlyng dea of the orgnal PCP algorthm s to allow a task to a mutex only f t can make sure that all mutexes that the task and ts hgher prorty tasks may use are not ed by lower prorty tasks. If not t forces the task to wat for those mutexes to be ed. To realze ths dea Rakumar et al. ntroduced the noton of a prorty celng and assocated t wth each mutex [5]. We defne PCP under PTS wth prorty celngs by combnng an offlne celng protocol and an onlne ng protocol n a smlar manner as n [6]. Protocol : PC-PCP. Offlne celng protocol CP. Each mutex s assgned a prorty celng whose value s gven by ϕ( = max{π τ Ψ } where Ψ s a set of tasks that may use mutex. Onlne ng protocol P. A system celng whch s a system-wde schedulng attrbute s dynamcally set to the maxmum of prorty celngs of all mutexes beng ed n the system. P. In order for task τ to enter ts crtcal secton π should be hgher than the system celng. P3. Inhertng effectve prortes If hgh prorty task s bed by low prorty task wth π H > γ task nherts p H from task as ts effectve prorty. P4. Recoverng effectve prortes When task exts from a crtcal secton task recovers p that t had before enterng that crtcal secton. In ths defnton of PCP under PTS effectve prortes are used for prorty nhertance (as specfed n P3 and P4 whle regular prortes are used for celngs of mutexes (as specfed n CP and P. It s qute straghtforward to use effectve prortes for prorty nhertance snce t s a mere adopton of BPI to solve the prorty nverson problemwe now show that PC-PCP prevents dead transtve bng and chaned bng. To begn wth we ntroduce a ng rule that can guarantee the avodance of dead transtve bng and chaned bng. Then we show our PCP defnton satsfes ths rule. ockng Rule. Task τ s allowed to a mutex only f all mutexes that may use are not ed by lower prorty tasks where π H π. Theorem. Conformng to ockng Rule guarantees the preventon of dead transtve bng and chaned bng. Proof. Conformng to ockng Rule ensures that a task cannot enter ts crtcal secton untl all mutexes t may use are ed. Therefore crcular watng cannot occur and thus dead s prevented. To show that conformng to ockng Rule guarantees the preventon of transtve and chaned bng we show that a task s bed at most once by at most one task under the ockng Rule. Suppose that task τ attempts to a mutex whle there s preempted task that has ed mutexes that may be used by hgher prorty or preempton threshold task where π H π. Then the ockng Rule forces task τ to get bed frst and wat for to those mutexes. Consequently there s always at most only one such task that s mutexes that may be used by where π H π. Accordngly whenever a task arrves t sees at most one (lower prorty task that has acqured mutexes t may use. Therefore t s guaranteed that a task s bed (to acqure ts mutexes at most once (when t frst tres to any mutex and by at most one lower prorty task. Therefore transtve and chaned bng cannot happen. Theorem. PC-PCP conforms to ockng Rule. Proof. Suppose that the PC-PCP does not conform to ockng Rule. Then task τ may a mutex when there s a ed mutex H that may be used by task where π H π. However accordng to CP of Protocol the prorty celng of H ϕ( H s equal to π H. ={ ={ H H H H ={ ={ ={ ={ γ π γ π π H γ π H γ γ γ H H arrve H H arrve (attempt to c bed by unnecessary bng t 0 t t t 3 t 4 t 5 t 6 t 7 t 0 t t t 3 t 4 t 5 t 6 t 7 (a Fgure 6. Examples: PCP under PTS usng (a prorty celngs and (b preempton threshold celngs. (b

7 When task τ attempts to any mutex the system celng equals ϕ( H = π H by P. Therefore τ should be bed snce π s not hgher than π H by P. Ths s a contradcton. Fgure 3 (b Fgure 4 (b and Fgure 5 (b llustrate how PCP prevents transtve bng chaned bng and dead respectvely. We have seen that n PCP a task can be bed only when t tres to enter ts crtcal secton for the frst tme: once a task successfully acqures any of ts mutexes t wll never get bed agan. Ths obvously mples that a task can be bed at most once by at most one lower prorty task. In PCP under PTS a task can encounter one of four forms of bng: ( drect bng ( push-through bng (3 celng bng [5] and (4 PTS bng. A task encounters celng bng when t attempts to enter a crtcal secton wth ts prorty not greater than the system celng. Fgure 3 (b Fgure 4 (b and Fgure 5 (b show examples of celng bng n PTS. Ths helps prevent dead transtve bng and chaned bng. 4. PCP under PTS wth Preempton Threshold Celngs It s not obvous why we used regular prortes to defne celngs of mutexes nstead of preempton threshold celng n Secton 4.. In fact we can use preempton threshold celngs for that purpose and defne another verson of PCP under PTS accordngly. The result s PTC-PCP. It s the same as PC-PCP of Protocol except that the prortes of CP and P of Protocol are replaced wth preempton thresholds. ockng Rule. Task τ s allowed to a mutex only f all mutexes that may use are not ed by lower prorty tasks where γ H γ. Theorem 3. Conformng to ockng Rule guarantees the preventon of dead transtve bng and chaned bng. Proof. Ths can be proved n a manner smlar to Theorem by substtutng prortes wth preempton thresholds. Theorem 4. PTC-PCP conforms to ockng Rule. Proof. Ths can be proved n a manner smlar to Theorem by substtutng prorty celngs of Theorem wth preempton threshold celngs and ockng Rule wth ockng Rule. 4.3 Comparson between PC-PCP and PTC- PCP Now we wll show that PC-PCP performs better than PTC-PCP wth respect to run-tme costs and the average response tme of a task set. The latter may ( ncur unnecessary context swtches and ( lead to longer response tmes due to unnecessary bngs. In most cases of practcal nterest a task has a preempton threshold that s no less than ts fxed prorty so as to avod unnecessary context swtches. In [] a task s even assgned the maxmum possble preempton threshold. Ths s ndeed a desrable heurstc to reduce unnecessary preemptons n preemptve fxed-prorty schedulng. However ths heurstc may not work well n PTC-PCP. In PTC- PCP wth ths heurstcs the system ends up wth a large number of tasks assgned the maxmum preempton threshold whch often forces hgh prorty tasks to serously suffer from celng bng. Fgure 6 demonstrates the stuaton. Suppose there are three tasks and wth γ π π H and γ =γ H. At t task acqures and then task arrves and preempts task at t. At t 3 t attempts to acqure H. At that pont n tme the system celng s equal to ϕ(. If we adopt prorty celngs (PC-PCP as depcted n Fgure 6 (a the system celng at t 3 s π. Snce π H > π task acqures H and contnues to run at t 3. On the other hand f we adopt preempton threshold celngs (PTC-PCP as depcted n Fgure 6 (b the system celng at t 3 s γ. Snce γ H s not greater than γ task gets bed at t 3 and resumes at t 4. Thus two extra context swtches occur at t 3 and t 4. oreover the response tme of task becomes longer n Fgure 6 (b than n Fgure 6 (a due to unnecessary bng at t 3. When runnng task τ tres to enter ts crtcal secton n PTS there s a case where s bed unnecessarly only n PTC-PCP: when the preempted task wth γ π H has acqured mutex l whch may be requested by τ l wth π l γ H and γ l γ H. Ths type of celng bng does not contrbute to preventng dead transtve bng or chaned bng snce ths bng s for mutexes that may be requested by lower prorty tasks. For every such case there are two addtonal context swtches n PTC-PCP as compared to PC-PCP. Note that such cases tend to be very frequent due to maxmum preempton threshold assgnment polcy n PTS. From ths observaton we recommend PC-PCP for obvous reasons: to avod unnecessary context swtches and to reduce the response tmes of hgher prorty tasks. 4.4 Schedulablty Analyss of PC-PCP For the schedulablty analyss of PC-PCP we adopt the worstcase response tme analyss n [0]. Under PTS the sets of nterferng hgher prorty tasks before and after a task gets the CPU are dfferent. Therefore for each task τ we should analyze ts start tme S and fnsh tme F separately. The equatons for the response tme analyss of PCP under PTS for task τ are as follows. β = max B γ π γ π > π 0 f Φ = φ { z k :: ϕ( k π } otherwse { C + β } C + β = max ( n n S + S = max { B β } + + C T (3 π > π 0 f B = 0 or β 0 δ = (4 otherwse (

8 F n+ = S + C + π > γ F T n S + C + β δ T (5 R = F (6 In PCP a task may be bed once n one of three forms of bng: push-through drect and celng bng. The worst case bng duraton for these types of bng for task τ (β s formulated n Equaton ( where z k s the duraton of the crtcal secton of task τ guarded by mutex k. Note that f the set of mutexes that task τ may use s empty (Φ =0 the bng tme under PCP s zero. Addtonally n PTS a task can experence PTS bng. The worst-case duraton of PTS bng for task τ s formulated n Equaton (. The start tme of task τ (S s formulated n Equaton (3: a task may be bed once n ether PTS bng or push-through bng before ts executon snce ( both bngs are caused by the same runnng task when the task arrves and ( the sets of tasks that can cause PTS bng and push-through bngs are mutually exclusve as shown n Equatons ( and (. The fnsh tme of task τ (F s formulated n Equaton (5 where δ s calculated from Equaton (4: task τ can be bed once agan durng ts executon n ether drect or celng bng. As shown n Equaton (4 ths type of bng (β δ becomes zero ( f PTS bng cannot occur (B = 0 or ( f the PCP bng tme of the task causng the PTS bng s not zero (β 0. Note that f task τ has encountered push-through bng or the task that caused PTS bng ( has encountered PCP bng (β 0 drect or celng bng cannot occur. 5. INIIZING CONTEXT SWITCHES In PCP a task can be bed once when t attempts to enter a crtcal secton. Alternatvely f we gve a task a chance to be bed when t s released for the frst tme n ts perod t wll never be bed agan durng ts executon. If we choose to use ths approach we can reduce two context swtches assocated wth each bng of a task n PCP. Ths alternatve whch s already wdely used n practce s called the mmedate nhertance protocol (IIP or the PCP emulaton protocol wth flag _POSIX_THREAD_PRIO_PROTECT n IEEE POSIX 003.c [9]. In ths secton we defne two versons of IIP under PTS: one wth prorty celngs and the other wth preempton threshold celngs. We refer to the former as PC-IIP and the latter as PTC-IIP. Then we nvestgate ther propertes compare them and present schedulablty analyss. 5. IIP under PTS wth Prorty Celngs The underlyng dea of the orgnal IIP algorthm s to allow a task to start ts executon only f t can make sure that all mutexes that the task and ts hgher prorty tasks may use are not ed by lower prorty tasks. If not t forces the task to wat for those mutexes to be ed. IIP bears many smlartes and benefts wth PCP. It can prevent prorty nverson dead transtve bng and chaned bng. oreover t can reduce the number of context swtches wthout sacrfcng the worst-case response tme. As n PCP we can defne two versons of IIP: PC-IIP and PTC- IIP. PC-IIP uses effectve prortes for prorty nhertance and regular prortes for prorty celngs of mutexes. Its offlne celng protocol and onlne ng protocol are presented below. Protocol 3: PC-IIP. Offlne celng protocol CP. Each mutex s assgned a prorty celng gven by ϕ( = max{π τ Ψ } where Ψ s a set of tasks that may use mutex. Onlne ng protocol P. Inhertng celng If task τ c acqures a mutex ts effectve prorty s set to p c = max{p c ϕ( ξ c } where ξ c s a set of mutexes that are currently ed by τ c. P. Recoverng effectve prortes When task τ c exts from a crtcal secton task τ c recovers p c that t had before enterng that crtcal secton. Whle the offlne celng protocol (CP s the same as that of PC- PCP the ng protocol (P and P s much more smplfed. Ths s because IIP forces prorty nhertance whenever a task s a mutex whle PCP does so only when a task bs a hgher prorty task. It s obvous that our PC-IIP defnton prevents prorty nverson dead transtve bng and chaned bng snce IIP s merely a specal case of PCP. ater we compare IIP wth PCP and dscuss the advantages of IIP over PCP. arrve bed by ={ ={ H H H H ={ ={ ={ ={ γ γ π π π H π H γ γ γ γ H H H H unnecessary bng t 0 t t t 3 t 4 t 5 t 6 t 7 Fgure 7. Example: IIP under PTS wth preempton threshold celng. 5. IIP under PTS wth Preempton Threshold Celngs As mentoned above the IIP under PTS can be defned wth ether prorty celngs (PC-IIP or preempton threshold celngs (PTC- IIP. We compare these two versons of IIP defntons usng the same example task set shown n Secton 4.3. Fgure 6 (a can be reused to llustrate IIP wth prorty celngs. Fgure 7 shows an example of PTC-IIP. As n PCP under PTS PTC-IIP yelds extra

9 bngs thus makes the response tmes of hgher prorty tasks longer. On the other hand note that the context-swtchng overhead remans the same n the two versons snce bng n IIP does not accompany context swtches. As n PCP we recommend PC-IIP over PTC-IIP. 5.3 IIP vs. PCP The most strkng dfference between IIP and PCP s that a task n IIP can encounter only celng bng: there s nether drect bng nor push-through bng n IIP. The number of context swtches ncurred by IIP can be as low as a half of the number ncurred by PCP. The best effcency under IIP occurs when every task n the system enters at least one crtcal secton. On the other hand f qute a few tasks do not enter a crtcal secton at all IIP may yeld extra bngs. In ether case the number of context swtches n IIP s always lower than n PCP. Ths s because bng n IIP does not accompany context swtches snce t always occurs before a task starts executon. However t s also true that the extra bngs encountered by hgh prorty tasks ncrease ther average response tmes n IIP. 5.4 Schedulablty Analyss of PC-IIP We provde the schedulablty analyss for PC-IIP. In IIP under PTS a task can be bed only once before ts start tme. Snce a task can be bed even f t does not enter any crtcal secton before ts start tme the equaton for bng tme β n IIP s formulated as Equaton (7. On the other hand snce a task s not bed durng ts executon the PTS bng n IIP under PTS s formulated as Equaton (8 and the fnsh tme s formulated as Equaton (9. Wthout these the formulatons for S and R n Equatons (4 and (6 n Secton 4.3 are adopted as they are. β = max { z :: ϕ( π } γ π k k (7 { } B = C max γ π > π (8 n+ = S + C + π > γ F F T n S + C T (9 6. CONCUSIONS In spte of the prolferaton of obect-orented desgn methodologes n contemporary software development ther applcaton to real-tme embedded systems has been lmted for the lack of proper real-tme schedulng theory that can be seamlessly ntegrated nto these methods. Specfcally popular preemptve fxed prorty schedulng cannot be drectly used n real-tme obect-orented desgn methodologes largely owng to ts excessve run-tme overhead. The preempton threshold schedulng has been recently suggested to ths end snce t mproves both run-tme overhead and schedulablty. Unfortunately t lacks real-tme synchronzaton capabltes. To solve ths problem n ths paper we have adopted three wellknown real-tme synchronzaton protocols and ntegrated them nto the preempton threshold schedulng. They are the basc prorty nhertance protocol (BPI the prorty celng protocol (PCP and the mmedate nhertance protocol (IIP. We have also presented ther schedulablty analyses. Snce each task under PTS has two schedulng attrbutes t s not ntutve durng the ntegraton whch schedulng attrbute should be used for prorty nhertance and for prorty celngs of mutexes. To clarfy ths problem we have ntroduced the noton of the effectve prorty whch s conceptually a task prorty that s used by the kernel scheduler for selectng a task to be dspatched. Wth ths we have dentfed the prorty nverson problem under PTS and presented the BPI protocol under PTS that avods such prorty nverson. Snce BPI alone cannot prevent dead we have also presented PCP and IIP under PTS. In these protocols we used effectve prortes for prorty nhertance and regular prortes for prorty celngs of mutexes. We have shown that two protocols wth prorty celngs yeld the smaller number of context swtches and shorter response tmes for hgher prorty tasks than those wth preempton threshold celngs. We have also shown that IIP further reduces the number context swtches compared to PCP. 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