Parallel Scheduling for Cyber-Physical Systems: Analysis and Case Study on a Self-Driving Car

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1 Parallel Schedulng for Cyber-Physcal Systes: Analyss and Case Study on a Self-Drvng Car Junsung K, Hyoseung K, Karthk Lakshanan, Ragunathan (Raj) Rajkuar Real-Te and Multeda Systes Laboratory, Carnege Mellon Unversty, Pttsburgh, PA Google Inc., Mountan Vew, CA {junsungk, hyoseunk, raj}@ece.cu.edu, karthksngara@gal.co ABSTRACT As the coplexty of software for Cyber-Physcal Systes (CPS) rapdly ncreases, ult-core processors and parallel prograng odels such as OpenMP becoe appealng to CPS developers for guaranteeng telness. Hence, a parallel task on ult-core processors s expected to becoe a vtal coponent n CPS such as a self-drvng car, where tasks ust be scheduled n real-te. In ths paper, we extend the fork-jon parallel task odel to be scheduled n real-te, where the nuber of parallel threads can vary dependng on the physcal attrbutes of the syste. To effcently schedule the proposed task odel, we develop the task stretch transfor. Usng ths transfor for global Deadlne Monotonc schedulng for fork-jon real-te tasks, we acheve a resource augentaton bound of In other words, any task set that s feasble on unt-speed processors can be scheduled by the proposed algorth on processors that are 3.73 tes faster. The proposed schee s pleented on Lnux/RK as a proof of concept, and ported to Boss, the self-drvng vehcle that won the 007 DARPA Urban Challenge. We evaluate our schee on Boss by showng ts drvng qualty,.e., curvature and velocty profles of the vehcle. Categores and Subject Descrptors D.4 [Software]: Operatng Systes; D.4.7 [Operatng Systes]: Organzaton and Desgn Real-te systes and ebedded systes; F.1 [Theory of Coputaton]: Coputaton by Abstract Devces; F.1. [Coputaton by Abstract Devces]: Modes of Coputaton Parallels and concurrency; I..9 [Artfcal Intellgence]: Robotcs Ths work was supported n part by the Natonal Scence Foundaton and n part by the US Departent of Transportaton. Ths author contrbuted to ths work whle he was at Carnege Mellon Unversty. Persson to ake dgtal or hard copes of all or part of ths work for personal or classroo use s granted wthout fee provded that copes are not ade or dstrbuted for proft or coercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc persson and/or a fee. ICCPS 13 Aprl 8-11, 013, Phladelpha, PA, USA. Copyrght 013 ACM /13/04...$15.00 Fgure 1: A oton plannng algorth for autonoous drvng Autonoous vehcles 1. INTRODUCTION Wth cyber-physcal systes (CPS), such as edcal devces, aerospace systes, sart grds, nuclear power plants, robots and transportaton vehcles, becong ore popular, deands for new functonalty features ultply [8]. For exaple, actve safety optons such as adaptve cruse control, brake assst, collson avodance, lane departure warnng, sgn detecton and tracton control are not rare anyore n recently bult vehcles. We, n fact, expect these CPS functonaltes to be readly avalable even n d-range cars. Wth ths trend, ebedded real-te systes are ndspensable n order to sense the physcal envronent, process data n real-te, control the actuators n a desrable anner and ontor the tng of the whole executon chan for ensurng safety. Autonoous drvng [31, 10, 6, 16, 30] s an appealng eergng CPS technology. In an autonoous car, oton plannng, sensor fuson, coputer vson and other artfcal ntellgence algorths ust run n real-te; however, the CPU-hoggng nature of those algorths poses challenges n guaranteeng ther telness. The tng challenge can be addressed by the fact that ost algorths for autonoous drvng are parallelzable. A plannng algorth of a self-drvng car can proft fro parallelzed tasks coposed of nuerous threads. The oton

2 plannng algorth calculates the best path for the vehcle to follow aong a yrad of potental paths. Ths algorth can be expedted by parallelzng the cost calculaton for each path. The ore paths the algorth goes through, the better drvng qualty wll be. Fgure 1 s a screenshot of the operator nterface for Boss, whch won the 007 DARPA Urban Challenge [31] showng a oton plannng algorth n operaton. In the fgure, the ultple lnes cong out fro Boss represent possble paths whch Boss ay follow, where each lne s generated by a parallel thread of the oton plannng algorth. When all threads are copleted, they erge nto a aster thread that selects the best path. It should be noted that the nuber of threads can vary dependng on the physcal condtons such as the shape of the road, the nuber of detected obstacles and the speed of the vehcle. A percepton subsyste of a self-drvng car can also beneft fro parallel tasks. In order for the vehcle to understand ts surroundngs, the percepton subsyste should be able to process assve aounts of data fro varous types of sensors. Boss, for exaple, anages ndependent segents fro ts Velodyne HDL-64 LIDAR before fusng the wth other sensor data. Then, the vehcle can classfy and track the detected obstacles, whose nuber has a ajor pact on how any parallel threads are spawned by the percepton subsyste. The autootve ndustry has already started ovng towards the ult-core processors for hgher perforance [, 14]. AUTOSAR, a wdely used autootve software nfrastructure, supports ult-core processors [4]. In addton, parallel prograng odels lke OpenMP [1] utlze ultple processng cores to guarantee concurrent executon. We beleve that other CPS applcaton doans wll follow ths trend sooner rather than later. There has been relatvely lttle research on tacklng challenges n schedulng parallel real-te tasks. In [1], Lakshanan et al. proposed a parallel task odel and a parttoned fxed-prorty schedulng algorth on a ult-core processor, but the nuber of threads could not exceed the nuber of gven processng cores. In [9], Safullah et al. proposed a ore generalzed parallel real-te task odel whch allows dfferent fork-jon segents of a task to have a dfferent nuber of threads. Contrbutons: In ths paper, we extend the fork-jon realte task odel proposed n [1] so that an arbtrary nuber of threads can be scheduled, where the nuber of threads can vary dependng on the physcal attrbutes of the syste. To effcently schedule the proposed task odel, we also propose a task stretch transfor to schedule the task odel on a gven nuber of processng cores. Then, we prove that a resource augentaton bound of 3.73 s acheved when we use the task stretch transfor for global Deadlne Monotoc (DM) schedulng for fork-jon real-te tasks. The proposed schee s pleented on Lnux/RK [5] and ported to the self-drvng car Boss [31]. We evaluate our proposed schee on Boss by showng ts drvng qualty n ters of curvature and velocty profles of the vehcle wth an enhanced oton plannng algorth [17]. C 1 P C 3 T = D (v s ) P s 1 C s Fgure : A fork-jon real-te task odel s 1 (vs ) Organzaton: The rest of ths paper s organzed as follows. In Secton, we defne our fork-jon real-te task odel and descrbe the syste assuptons. We provde a schedulng algorth to handle parallel real-te tasks n Secton 3. The analyss usng resource augentaton bound for global DM schedulng follows n Secton 4. We, then, brefly explan n Secton 5 the odfcatons ade to Lnux/RK to support the proposed schee on a Lnuxbased syste. Secton 6 shows the curvature and velocty profles of a self-drvng car when our proposed schee s used. We descrbe prevous research relevant to our work n Secton 7, and, n Secton 8, we suarze our paper and dscuss future work.. SYSTEM MODEL AND ASSUMPTIONS Defnton: We consder a set of tasks τ coposed of n ult-threaded real-te tasks, and the gven set τ runs on a syste wth processng cores. τ s represented as τ : {, τ,..., τ n}, and the tasks n τ are sorted n nondecreasng order of task perods (deadlnes). Each task τ begns wth a sngle thread spawnng parallel threads, whch jon wth another sequental thread of τ. τ nterchanges ths pattern between parallel and sequental segents. The nuber of parallel threads depends on the physcal attrbutes of the gven syste v s R p, where p s the nuber of densons that capture aspects of the operatng envronent. Then, as depcted n Fgure, each task τ s represented as τ : ((C 1, (P, (v s)), C 3,..., (P s 1, s 1 (v s)), ), T, D), where C s s s the nuber of coputaton segents of τ. Snce τ starts wth a sequental segent and ends wth a sequental segent whle havng parallel segents n the ddle, s s a postve odd nteger. For 1 j s, the j th eleent s a parallel segent f j s an even nuber. Slarly, the j th eleent s a sequental segent f j s an odd nuber. j (vs) s the nuber of parallel threads for the jth segent when 1 j s. When j s an odd nteger, j (vs) s 1 and otted fro the representaton of τ above for ease of presentaton. When j s an even nteger, j (vs) s equal to or greater than 1 and represents the nuber of parallel threads spawned by the prevous segent. C j s the worst-case executon te of the jth segent n task τ on a unt-speed processor when the j th eleent s a sequental segent. Also, let τ j,1 denote the j th sequental segent of τ.

3 P j s the worst-case executon te of each thread run n the j th segent of task τ on a unt-speed processor when the j th eleent s a parallel segent. For parallel segents of τ, each thread of parallel threads s represented as τ j,k, where k vares fro 1 to j (vs). D s the relatve deadlne to ts release te. T s the perod of τ. An plct deadlne s assued,.e., T = D. Applcaton Exaples to Autonoous Drvng: The oton plannng algorth of Boss uses OpenMP to parallelze ts cost calculatons to fnd the best path. Snce the algorth takes ts nputs: the road rules, the road shape, the vehcle speed, the lst of statc obstacles and the lst of dynac obstacles, we defne v s as < RoadRule, RoadShape, V ehcleinfo, StatcObstacles, DynacObstacles >. Ths vector v s s then used to decde the nuber of parallel threads accordngly. The percepton algorth of Boss leverages pthread to expedte ts executons of processng perceved objects. We therefore defne v s for the percepton algorth as <SensorLst, SensorP ose, RawSensorDataLst, V ehclep ose>. In ths paper, we consder the nuber of threads wthn each parallel segent not to exceed the axu value of j (vs) for vs Rp. For ease of presentaton, therefore, we use j nstead of j (vs). Assuptons: Each task τ s assued to generate an nfnte seres of ndependent jobs. The release te of the j th segent of each job of τ should be after the copleton te of the (j 1) th segent 1. Therefore, f the j th eleent of τ s a sequental segent, all parallel threads of (j 1) th segent of τ should coplete before the j th eleent of τ starts. We assue that all jobs are preeptable wth neglgble cost. We also assue that there s neglgble graton cost when a job s grated fro a core to another. Ternology: Usng ths odel, we defne the axu nuber of threads of τ, whch s the axu value aong j of τ. Forally, = s ax j=1 j The axu executon length of a task τ on a unt-speed processor s defned as: C = s 1 j=0 C j+1 + s 1 j=1 j P j where, C represents the response te on a unt-speed sngle core processor when run alone. The frst ter corresponds to sequental task segents and the second ter corresponds to fork-jon segents. To defne the nu executon length of a task τ, we have to consder two dfferent cases: (1) and () >. For the frst case, the nu executon length s defned as η = s 1 j=0 Cj+1 + s 1 j=1 P j, where η s the 1 We wll use the ters jobs and tasks nterchangeably where the dstncton s not of portance. response te when each sngle thread of τ can use a core exclusvely. When >, the defnton above does not hold good because soe threads ust be seralzed. When >, therefore, we defne the nu executon length η as: η = s 1 j=0 C j+1 + s 1 j=1 j P j (1) The defnton above can also be used when because j = 1 when. Hence, t holds good for both cases. For ease of presentaton, we also let P = s 1 j=1 P j, j whch s the executon requreent of the parallel segents contrbutng to η. The task odel n ths paper s extended fro the forkjon task odel proposed n [1]. The two an dfferences between the prevous one and ths odel are that (1) our odel places no ltaton on the nuber of threads, and () our odel allows dfferent nuber of threads per parallel segent. Hence, ths odel s ore practcal. 3. SCHEDULING FORK-JOIN REAL-TIME TASKS It was shown n [1] that there are unschedulable task sets where the total utlzaton of the taskset s slghtly greater and very close to 1 even though there are processng cores. In other words, deadlnes can be ssed even though only 1 of avalable cycles s used. Although approaches nfnty, the schedulablty does not change [1]. Ths worst-case behavor contnues to hold good for the proposed odel n ths paper because t s an extended for of the task odel proposed n [1]. In ths secton, we frst consder a schedulng ethod to handle fork-jon real-te tasks on a processor wth a gven nuber of cores. Then, we propose the task stretch transfor to deal wth our enhanced task odel. 3.1 Runnng Fork-Jon Real-Te Tasks on CPU Cores Consder a task τ τ runnng on processng cores. If the axu nuber of parallel threads aong all parallel segents n τ s less than the nuber of processng cores, we can drectly apply the task transforaton algorth descrbed n [1]. If exceeds the nuber of processng cores, then the seralzaton of soe parallel threads ust happen as depcted n Fgure 3, where a task eets ts deadlne on a quad-core processor, but not on a dual-core processor. Proposton 1. A fork-jon real-te task τ requres at least the nu executon length η unts of te on CPU cores to eet ts deadlne. We obtan the nu executon length η of τ depcted n Fgure 3 as 10 on a quad-core processor and 16 on a dual-core processor fro Equaton 1. Fro Proposton 1, we can show that the gven task s nfeasble on a dual-core processor because η on a dual-core processor s greater than ts deadlne. We also call our proposed odel a fork-jon task odel unless stated otherwse.

4 1,1,1,,3,4,5,6,7,8 3,1 te (a) On a quad-core processor : (, 3, 8,, 15, 15) sses ts deadlne on a dual-core processor. 1,1,1,,3,4,5,6,7,8 3, (b) On a dual-core processor Fgure 3: : ((, (3, 8), ), 15, 15) sses ts deadlne on a dual-core processor, but not on a quad-core processor. 3. The Task Stretch Transfor We propose a task transforaton algorth stretch n Algorth 1. It breaks down a fork-jon real-te task nto a set of tasks. Ths set s coposed of a long task called a aster strng and a bunch of constraned-deadlne tasks wth D < T. Ths set can be scheduled usng any schedulng algorth supportng conventonal sngle-threaded tasks such as global DM, global EDF [1] and FBB-FFD [13]. In Algorth 1, when a new constraned-deadlne task s created, t s represented as τ : (C, D, φ), where C s the worst-case executon te, D s the relatve deadlne, and φ s the release offset. When a parallel thread s erged nto an exstng task, we use as a sybol and τ : (C) as the thread added to the exstng task. Mergng a thread does not change ether the deadlne or the offset of the exstng task. In ths algorth, we ade a sall change on how to use the odulo functon. k od q returns q f k od q = 0. We use two paraeters f and q n Algorth 1. f s the rato of the parallel executon requreents P to the slack of the task T η. We use ths value to evenly dstrbute the slack to each parallel segent. q s the nuber of parallel threads after a task s processed by Algorth 1. In other words, at any pont of te t, τ stretch wll have at ost q concurrent runnng threads on cores. It should be noted that the deadlne assgnent for the q th thread s dfferent fro others because we splt the thread so that we can avod the worst-case scenaro explaned n [1]. The algorth s an extenson of the task stretch transforaton proposed n [1]. The stretch transforaton can handle ore general cases: (1) when the nuber of parallel threads exceeds the nuber of cores, and () when the nuber of parallel threads of each segent s dfferent. The proveents can be descrbed as follows: Algorth 1 Stretch (τ) Input: τ: a fork-jon real-te task Output: τ stretch : a stretch ed task set 1: τ aster () : {τ cd } {} 3: f C T then 4: The task can run on a sngle core 5: for j = 1 to s 1 do 6: τ aster τ aster 7: for k = 1 to j 8: τ aster 9: τ aster 10: else do τ aster τ j 1,1 τ aster τ s,1 τ j,k : (C s : (C j 1 ) : (P j ) 11: Stretch the task to ts deadlne T 1: f η s 1 j=1 j j P ) 13: q n (, ) f 14: for j = 1 to s 1 do 15: τ aster τ aster τ j 1,1 : (C j 1 ) 16: 1) Coalesce threads so that the total nuber of parallel threads s less than q 17: for k = 1 to j do 18: f k od q = 1 then 19: Part of the aster strng 0: τ aster τ aster τ j,k : (P j 1: else f τ j,k od q / {τ cd } then : Create a new parallel thread 3: D j 4: φ j (1 + f ) j j 1 l=0 Cl+1 } {τ cd j P + j 1 l=1 Dl ) 5: {τ cd } τ j,k od q : (P j, D j, φj ) 6: else f τ j,k od q {τ cd } then 7: Part of the exstng threads 8: τ j,k od q τ j,k od q τ j,k : (P j ) 9: ) Splt aong the q -th thread and the aster strng 30: f τ j,q } then 31: {τ cd } τ j,q 3: τ aster τ aster {τ cd } {τ cd f ) j ) 33: Create a new parallel thread 34: D j,q 35: φ j 36: {τ cd 37: τ aster P j (1 + f ) j j 1 l=0 Cl+1 } {τ cd f ) j 38: return τ stretch j P, D j,q τ aster τ s,1 := ( τ aster τ j,q : ((f j P + j 1 l=1 Dl } τ j,k : ((1 + f, φ j ) : (C s ), {τ cd } ) If the nuber of parallel threads wthn a fork-jon segent exceeds the nuber of CPU cores, all parallel threads τ j,k wth the sae value of (k od q ), where 1 k j, coalesce nto the thread τ j,k od q. Ths step guarantees that the nuber of parallel threads does not exceed the nuber of processng cores after the task transforaton. Based on the new worst-case executon te of the erged threads of each parallel segent, a constraned deadlne proportonal to (1+f ) s assgned to each par- allel segent by the algorth. Accordngly, an offset s also deterned so that parallel threads are released at the rght te nstants. Fgure 4 shows an exaple of the task stretch transforaton wth a task : ((, (3, 8), ), 15, 15). The task has 8 parallel threads, and t has a slack of 5 because the nu executon length η 1 s 10. Usng the slack, a porton of τ,4 1 and τ,8 1 are scheduled wth the aster strng.

5 1,1,1,,3 3,1 + Quad-core Processor 1,1,1,5,4,8 3,1 τ 1 C on Adahl s law [], n(, = P holds good because all ) the segents are runnng n parallel. Snce we assue a forkjon odel that has non-zero seral segents, the deal case C cannot be acheved. However, approachng P to n(, ) s desrable to fully utlze parallels.,4,5,6,7,8 0 5 te Stretch* T 1 = 15 η 1 = 10 f 1 = 5 6 q 1 = 4 te,,3 τ 1,4,6, Fgure 4: The task stretch transforaton exaple wth : ((, (3, 8), ), 15, 15) 4. RESOURCE AUGMENTATION BOUND ANALYSIS FOR GLOBAL DEADLINE MONOTONIC SCHEDULING In ths secton, we derve the resource augentaton bound of global DM schedulng for the task odel descrbed n Secton 3. To the best of our knowledge, ths s the frst result of resource augentaton bound of global DM schedulng for parallel real-te tasks. For ths approach, we use a denstybased schedulablty test proposed n [8] gven below. Theore 1 (fro [8]). A set of perodc or sporadc tasks wth constraned deadlnes s schedulable wth Deadlne- Monotonc prorty assgnent on processors f: λ su (1 λax) + λax () where, λ su s the su of the densty of each task n the taskset, λ ax s the axu value of task denstes, and a densty λ s a rato of the deadlne of a task to ts worst-case executon te. Let λ stretch denote the su of the densty of each task n the stretched taskset τ stretch. As specfed n Algorth 1, two cases, (1) C T and () C > T should be consdered to understand the propertes of λ stretch. Two correspondng leas are presented next. Lea 1. For a fork-jon real-te task τ, the densty of the resultng stretched task τ stretch s bounded by C T f C T. Proof. For the case of C T, we use the fact that the executon requreent and T (= D ) of both τ and τ stretch are equal. Then, fro the defnton of densty, C T. Before nvestgatng a fork-jon real-te task τ wth C > T, we assue that τ s provded wth a level of parallels so that P s satsfed. In the deal case, based C n(, ) Lea. For a fork-jon real-te task τ, the su of the densty of the resultng stretched τ stretch s bounded by C T η f C > T. Proof. For the case of C > T, t should be noted that the output of the algorth s a set of tasks coposed of a aster thread τ aster and several constraned deadlne tasks {τ cd }. Hence, the followng nequalty holds good: λ stretch λ aster + τ {τ cd } Snce the worst-case executon te of τ aster s less than T, λ aster 1 fro the plct deadlne assupton. It s known that there wll be at ost q concurrent runnng threads ncludng the aster thread at any pont of te t. We ensure ths by assgnng an offset whenever a new parallel thread s created n Algorth 1. The offset also guarantees that only one segent s actve at a te. Thus, the densty of τ can be substtuted wth the densty of a segent that has the largest value aong the denstes of the segents of τ. Let P ax s 1 = axj=1 j j P. We frst consder the case of q >. When q threads are sultaneously runnng, for the q 1 constraned tasks, there wll be q parallel threads wth the executon te of P ax and the relatve deadlne of (1 + f )P ax. There wll also be a parallel thread wth the executon te of (1 + f f )P ax and the relatve deadlne of (1 + f )P ax. Therefore, f we let P = s 1 j=1 P j, the followng nequaltes are satsfed: τ {τ cd } λ j ax (q )P + (1 + f )P ax (q 1) (q 1)P = (1 + f ) (P + T η ) λ (1 + f f)p ax (1 + f )P ax We then consder the case of 0 < q. When q s 1, t eans that τ can run on a sngle core. Therefore, we focus on the case of q =, whch eans that τ {τ cd } λ wll have only the task whch s splt. Therefore, τ {τ cd } λ = (1 + f f)p ax (1 + f )P ax 1 (1 + f ) P (q 1)P = (P + T η ) (P + T η )

6 Now, we consder both τ aster and {τ cd }. λ stretch (q 1)P P + T η + (q 1)P 1 + = (P + T η ) (P + T η ) (f + q)p (f + n(, ) f )P = = (P + T η ) (P + T η ) n(, )P (P + T η C ) T η Fro the nequalty above, the lea s proved. We defne a task called a heavy task that has a densty greater than or equal to 1 on a -speed processng core. Theore. Global Deadlne Monotonc schedulng of the fork-jon real-te task odel has a resource augentaton bound of 3.73 when each heavy task s assgned to ts own processng core. Proof. Consder a set of n fork-jon real-te tasks τ. We assue that the gven taskset s feasble on dentcal unt-speed processors, whch ples n C =1 T. Otherwse, the gven taskset s not feasble. Let there be k heavy tasks on a -speed processor. Under the task stretch transfor descrbed n Algorth 1, these are ether fully stretched tasks (C T ) or aster threads (C > T ). Both types of tasks have a deadlne equal to ther perod, and ther densty s at least 1 on a unt-speed processor by the defnton of a heavy task. Therefore, for the reanng n tasks: n =1 C T = n =1 C D = λ = λ su ( k) (3) n =1 We need to show that these reanng tasks are schedulable on (= k) processors of speed, where On a processor that s tes faster, the nu executon length η on a -speed processor s gven by η = s 1 j=0 C j+1 + s 1 j=1 j P j η T where, 1 n. Also, the axu executon length of τ on a -speed processor s C = s 1 j=0 where, 1 n. C j+1 + s 1 j=1 j P j = C Case (1): For each fully stretched task τ that s non-heavy on -speed processors, the densty s C T fro Lea 1 and Equaton 5. 1 (4) (5) C T 1 C 1 T Case (): Consder the constraned-deadlne taskset generated by stretch on -speed processors for task τ. Fro the perspectve of load, the total densty on -speed processors C s bounded by T η C / = 1 C T T 1 T fro Lea, Inequalty 4 and Equaton 5. λ su on -speed processors, therefore, s bounded by n 1 because λ su n 1 C =1 1 T = 1 C 1 =1 T fro 1 Inequalty 3. The aster threads for tasks that cannot be fully stretched are always heavy tasks snce they use up the entre T on the -speed processor. By the defnton of heavy tasks, λ ax s always upper bounded by 1 on -speed processors. Then, for usng Inequaltes and 3 and the cases consdered above, As, we get, ( 1 1 ) ( ( 1) 4 1 ( 1) 4 1 ( 1) ) Ths holds good for all processors usng GLOBAL SCHEDULING ON LINUX/RK We have desgned an operatng syste abstracton for anagng our parallel real-te task odel usng the resourcereservaton paradg. A parallel task n our odel s coposed of ultple threads. A thread called aster strng executes all sequental segents and a porton 3 of parallel segents. Parallel threads are spawned by the aster thread and execute the reanng porton of parallel segents. In order to represent the ultple threads and ther precedence constrants, our abstracton eploys the resource anageent enttes, resource set and reserve, ntroduced n resource kernels [7], where Resource set: A resource set corresponds to a parallel task. It s a contaner of ultple reserves. Reserve: A reserve represents the aount of CPU budget to be reserved on a sngle core or ultple cores. A reserve s specfed wth (C, T, D, φ): C s a worst-case executon te; T s a perod; D s a relatve deadlne; φ s a release offset. Fgure 5 shows the schedulng of a parallel real-te task on four cores wth the stretch transforaton. The parallel task has one parallel segent coprsng four threads. 3 Ths porton s obtaned by runnng Algorth 1.

7 offset: 0 : (, 6, 4,, 15, 15) 1,1,1,4 τ 1 3,1, Resource Set for Reserve: rsv 1 (15, 15, 15, 0) Reserve: rsv (6, 15, 13, ) pro: 3 (low) pro: NW ntersecton () (4) (5) (1) Parkng lot 4-way ntersecton spawned (offset: ),3 Reserve: rsv 3 (6, 15, 13, ) pro: (3) Boss starts here τ 1,4 te Reserve: rsv 4 (1, 15, 8, ) pro: 1 (hgh) SE ntersecton Fgure 5: CPU resource abstracton for a parallel task wth global DM schedulng Fgure 6: The ap followed by Boss The stretch transforaton splts the last thread of the parallel segent, τ,4 1, nto τ,4 1 and τ,4 1. Hence, τ,4 1 s assgned a relatve deadlne of 8 that s equal to the release offset of τ,4 1. The CPU usage and ts offset on each core can be represented as a reserve. Snce a reserve s equvalent to an ndvdual sequental perodc task, the global DM schedulng algorth can deterne the schedulng prortes for reserves. Then, we assgn reserves to threads so that each thread s scheduled wth the prorty and the release offset of the assgned reserve and consues the reserve s CPU budget. The aster strng thread, (,1 1 τ,1 1 τ 3,1 1 ), s assgned a reserve (rsv 1). The second and the thrd thread n the parallel segent, τ, 1 and τ,3 1, are assgned (rsv ) and (rsv 3), respectvely. The last thread τ,4 1 s assgned an ordered lst of reserves, (rsv 4 rsv 1). Ths eans that τ,4 1 frst uses rsv 4 s prorty and CPU budget, and when t uses up rsv 4 s budget, t contnues ts executon wth rsv 1 s prorty and reanng CPU budget. We pleented the abstracton for parallel tasks on Lnux/ RK [5], whch s based on the Lnux kernel. We used hrters to release threads at specfed offsets and to account the CPU usage of threads. When a thread uses up all reserves assgned to t, the abstracton enforces the CPU usage of the thread by suspendng t. The accountng and the enforceent of our abstracton can also be used for the easureent-based worst-case-executon-te estaton of threads n a parallel task, by checkng an occurrence of the enforceent wth a tentatve executon te. 6. CASE STUDY ON SELF-DRIVING CAR We studed the effcacy of our proposed schee usng a selfdrvng car platfor Boss. The latest oton plannng algorth runnng on Boss [17] s used for our evaluaton. The algorth consders the dstance to the next destnaton, the lateral offset of the car to the center of the lane, the longtudnal velocty, the longtudnal acceleraton, the lateral acceleraton and a lst of statc/dynac obstacles on the road where the vehcle s drvng. Wth the gven nforaton based on whch the nuber of parallel threads vares, the algorth generates curvature and velocty profles for the path whch the vehcle should follow. The plannng algorth s pleented usng OpenMP, and we evaluate the qualty of autonoous drvng by analyzng curvature and velocty profles of Boss (1) when the conventonal reservaton approach wth Lnux/RK [5] s used, () when the prevous task odel [1] s used, and (3) when our proposed task odel and algorth are used. We ran the plannng algorth on a sulaton cluster [3, 19] equpped wth an Intel Core 7 quad-core processor. Although we run the exact sae algorth on the vehcle, we easure the results on the sulaton cluster due to testng, convenence and safety consderatons. We ran a scenaro wth the layout of our test track located at Robot Cty n Hazelwood, Pttsburgh, PA, where we test the vehcle at straght ult-lane roads, curvy roads, ntersectons, U-turns and parkng lots. The exact sae scenaro fle s also used durng the feld test, but the tasks for recevng raw sensor data are replaced wth sulaton tasks. In Fgure 6, the test track for the scenaro s llustrated. Boss wll depart at the pont crcled n the ddle of Fgure 6. Boss wll follow the road, (1) cross a 4-way ntersecton governed by stop sgns, follow the straght road and () ake a left turn at NW ntersecton. Then, Boss wll (3) ake a left turn at SE ntersecton, proceed to NW ntersecton and (4) turn rght towards the curve arked wth (5) connectng to the long straght road. The scenaro s coposed of eght tasks: BehavorTask, MssonPlannerTask, OnRoadMotonPlannerTask, PrePlannerTask, RoadBlockageDetector, RobotClent, ServerTask and SpleControllerTask. The BehavorTask decdes what to do such as turnng, ntersecton handlng and lane changng. The MssonPlannerTask nteracts wth the stored ap to decde where to go. The OnRoadMotonPlanner- Task and the PrePlannerTask send trajectores to the vehcle controller. The RoadBlockageDetector works wth the BehavorTask so that the vehcle detects the blocked road and fnds an alternate route when needed. The SpleControllerTask receves the actuator coands and drectly nterfaces wth the vehcle hardware such as the accelerator, the brake and the steerng wheel. On the sulaton cluster, ths task operates n sulaton ode, and the ServerTask and the RobotClent behave as the vehcle hardware. In ths paper, our focus s on the OnRoadPlannerTask runnng the oton plannng algorth [17] wth OpenMP enabled. The task generates curvature and velocty profles for the vehcle hardware, so the lack of resources wll affect the control algorth, akng the car drve n an unstable anner. If the plannng algorth does not eet the deadlne, the steerng wheel, for exaple, jerks and the car goes to an unexpected place, whch can cause an accdent.

8 Curvature Velocty (/s) Te (s) Fgure 7: Curvature and velocty profles durng the entre journey of Boss llustrated n Fgure 6. Curvatu Velocty (/s) Te (s) Fgure 8: Curvature and velocty profles of Boss when conventonal resource reservaton s used. Velocty (/s) Te (s) Fgure 9: Curvature and velocty profles of Boss when prevously known technques [1] are used. Fgure 7 shows the autonoous drvng perforance,.e., the curvature and velocty profles collected fro the output of OnRoadMotonPlannerTask when the proposed task odel and algorth are used wth a varyng nuber of threads. We lt the axu nuber of threads to 50. The curvature graph shows when Boss akes turns; a negatve value eans a left rotaton of steerng wheel, and vce versa. For exaple, Boss arrves at the SE ntersecton n Fgure 7 around t = 65s, and that s the fourth valley n the curvature graph. Accordngly, we can see the velocty of Boss decreases to turn left. The bgger the absolute value of curvature, the steeper wll be the turn ade by Boss. Fro the perspectve of autonoous drvng qualty, a sudden control change on an actuator s not desrable. Fgure 8 shows an undesrable case when the conventonal

9 resource reservaton approach wth Lnux/RK s used. Snce the tradtonal Lnux/RK does not consder a parallel task odel, t assgns all chld threads nto a reserve allocated to a processng core. Snce ths ay prevent the plannng algorth fro runnng n parallel, the planner ay not be able to eet ts deadlne, whch s shown fro 130s to 150s n Fgure 8. The plannng algorth requres ore threads when a car s ovng faster and/or when a car s akng a sharp turn. The results shown, therefore, are consstent wth the property of the plannng algorth. Fgure 9 also shows the result when the odel of [1] s used, where only four threads can run n parallel because the sulaton cluster has a quad-core processor. For ths case, the velocty profles are fne, but the curvatures show soe jtters that can ake the vehcle unstable and also uncofortable for passengers. The results shown n Fgure 8 and 9 could be potentally dangerous on the real vehcle because the vehcle n the realworld ay slp, drft and crash. 7. RELATED WORK Snce Dhall and Lu [1] showed that RM and EDF schedulng could utlze only one processor regardless of how any processors a syste had, there has been extensve research on global real-te schedulng [3, 15, 6, 5, 7, 8, 9, 11], where a coprehensve survey can be found n [11]. It s well-known that the anoaly of global schedulng happens when a set of tasks has two types of tasks: tasks wth a low rato of the worst-case executon te to relatve deadlne and tasks wth a hgh rato of the worst-case executon te to relatve deadlne. Many algorths have been nvented to avod such cases, and correspondng schedulablty tests have been proposed. Usng our proposed task transforaton, any exstng global schedulng algorth can be appled to schedule parallel real-te tasks. In ths paper, we have used the schedulablty bounds for global DM proposed n [6, 9]. There has not been uch research on schedulng parallel real-te tasks [18, 1, 9, 4]. Lakshanan et al. [1] proposed a fork-jon real-te task odel coposed of alternatng sequental and parallel segents. They also provded the analyss and resource augentaton bound for the parttoned DM schedulng [13] of parallel real-te tasks usng the task stretch transforaton. The proposed ultprocessor schedulng algorth s shown to have a resource augentaton bound of 3.4, whch ples that any task set that s feasble on unt-speed processors can be scheduled by the proposed algorth on processors that are 3.4 tes faster. Our work s a generalzaton of ths odel and provdes a resource augentaton bound when global schedulng s used. Safullah et al. [9] also proposed a parallel synchronzaton odel that s also generalzed fro the fork-jon task odel n [1] so that a task can have an arbtrary nuber of threads per segent. Based on the proposed odel, a task decoposton ethod s used to decopose each parallel task nto a set of sequental tasks. The task decoposton acheves a resource augentaton bound of 4 and 5 when the decoposed tasks are scheduled usng global EDF and parttoned DM schedulng, respectvely. Our work focuses ore on global fxed-prorty schedulng and shows the evaluaton results easured fro a real-world pleentaton. More recently, Nelssen et al. [4] presented both offlne and onlne algorths to nze the nuber of cores to be used to schedule ult-threaded tasks usng a slar odel to the odel proposed n [9]. By usng schedulng algorths whch can guarantee the schedulablty of the gven tasks as long as the su of denstes of all the gven tasks s less than or equal to the nuber of processng cores, they obtaned a resource augentaton bound of. Our perspectve s dfferent fro thers n a sense that we schedule a set of tasks under a gven hardware constrant (the nuber of processng cores) rather than fndng hardware for the gven tasks. We also use global DM schedulng algorth ore coonly used n practce and show the evaluaton results obtaned fro a workng syste. Apart fro work usng the Thread odel entoned above, there has also been research based on gang schedulng, where all parallel coponents of the sae task should arrve and coplete at the sae te. Gang EDF [18] was proposed to address gang schedulng n the real-te context. Our work s dfferent fro ths n two ways: (1) our odel allows the parallel segents to be preepted durng the parallel executon, and () a dfferent nuber of parallel threads can be used. 8. SUMMARY AND FUTURE WORK To eet rapdly ncreasng deands for coplex cyber-physcal systes, we otvated the necessty of usng ult-core processors and correspondng parallel prograng odels such as OpenMP [1]. In partcular, eergng CPS such as a self-drvng vehcle can beneft sgnfcantly fro parallel real-te tasks allowng ultple copute-ntensve realte tasks to support deandng requreents. Thus, a self-drvng vehcle can odel ts physcal surroundngs n parallel and react to the n real-te. In ths paper, we proposed a fork-jon parallel real-te task odel, where the aount of parallel executons can vary dependng on the physcal attrbutes of the syste. The proposed task odel s transfored usng our stretch algorth. Wth global deadlne-onotonc schedulng, we obtaned a resource augentaton bound of 3.73, whch eans that any task set that s feasble on unt-speed processors can be scheduled by the proposed algorth on processors that are 3.73 tes faster. The proposed schee was pleented on Lnux/RK [5] as a proof of concept, and ported to Boss, the self-drvng car that won the 007 DARPA Urban Challenge [31]. On Boss, we evaluated our proposed schee that proved ts autonoous drvng qualty. Future work to be done ncludes supportng dynac changes of perods and executon tes of parallel real-te tasks. We already have early work on varyng perods [0], and the dynac nature of CPS wll be addressed usng ths odel cobned wth parallel tasks. Acknowledgents The authors would lke to thank Tanyu Gu and Junqng We for ther valuable coents on the case study. 9. REFERENCES [1] OpenMP. [] G. Adahl. Valdty of the sngle processor approach to achevng large scale coputng capabltes. In

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