Keynote: RTNS Getting ones priorities right

Transcription

1 Keynote: RTNS 2012 Gettng ones prortes rght Robert Davs Real-Tme Systems Research Group, Unversty of York

2 What s ths talk about? Fxed Prorty schedulng n all ts guses Pre-emptve, non-pre-emptve, deferred pre-empton Sngle processor, multprocessor Sporadc tasks, mxed crtcalty, probablstc executon tmes etc. Prorty assgnment Why s t mportant? What s an optmal assgnment? How do we fnd t? Is Optmal Prorty Assgnment enough? Can we optmse other thngs as well? Unsolved prorty assgnment problems 2

3 Prorty assgnment Why s prorty assgnment mportant Acheve a schedulable system when t otherwse wouldn t be Provde a schedulable system avodng hardware overprovson / maxmsng use of hardware resources Provde headroom for unforeseen nterference or overruns Example Controller Area Network (CAN) Used for n-vehcle networks Message IDs are the prortes 3

4 When prorty assgnment goes bad! From Darren Buttle s Keynote at ECRTS 2012 The myth of CAN bus Utlsaton You cannot run CAN relably at more than 30% utlsaton 1 1 Fgures may vary but not sgnfcantly Why? Message IDs.e. prortes assgned n an ad-hoc way reflectng data and ECU suppler (legacy ssues) as well as many other ssues, ncludng devce drver mplementaton 4

5 When prorty assgnment goes bad! Example: CAN Typcal automotve confg: 80 messages 10ms -1s perods All prorty queues x10,000 message sets Breakdown utlsaton Scale bus speed to fnd utl. at whch deadlnes are mssed 80% v 30% or less Frequency Random Prortes Optmal Prortes [R.I. Davs, S. Kollmann, V. Pollex, F. Slomka, "Schedulablty Analyss for Controller Area Network (CAN) wth FIFO Queues Prorty Queues and Gateways. Real-Tme Systems, 2012] Breakdown Utlsaton 5

6 System model Sngle processor, fxed prorty schedulng Scheduler chooses the hghest prorty ready task to execute Perodc / Sporadc task model Statc set of n tasks. Each task τ has a unque prorty C - Executon tme (bound) D - Relatve deadlne T - Mnmum nter-arrval tme or perod Varatons Implct / constraned / arbtrary deadlnes Pre-emptve / non-pre-emptve / deferred pre-empton schedulng Unque prortes or shared prorty levels 6

7 Schedulablty Schedulablty tests Determne f all jobs of a task (all tasks) can be guaranteed to meet ther deadlnes for all vald arrval patterns Suffcent f all of the tasksets that the test deems to be schedulable are n fact schedulable Necessary f all of the tasksets that the test deems to be unschedulable are n fact unschedulable Exact mples both suffcent and necessary Worst-case response tmes Schedulablty tests often compute the worst-case response tme R for each task and compare t wth the task s deadlne D to determne schedulablty 7

8 Defnton: Optmal prorty assgnment polcy For a gven system model, a prorty assgnment polcy P s referred to as optmal f there are no systems, complant wth the model, that are schedulable usng another prorty assgnment polcy that are not also schedulable usng polcy P. accordng to the test accordng to the test An optmal prorty assgnment polcy can schedule any system that can be scheduled usng any other prorty assgnment May also consder prorty assgnment polces that are optmal wth respect to a specfc (suffcent) schedulablty test [N.C. Audsley, "Optmal prorty assgnment and feasblty of statc prorty tasks wth arbtrary start tmes", Techncal Report YCS 164, Dept. Computer Scence, Unversty of York, UK, 1991.] [N.C. Audsley, On prorty assgnment n fxed prorty schedulng, Informaton Processng Letters, 79(1): 39-44, May 2001.] [R.I. Davs and A. Burns "Improved Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. Real-Tme Systems, (2011) Volume 47, Number 1, pages 1-40] 8

9 Early work on prorty assgnment 1967 Fneberg & Serln Two perodc tasks wth mplct deadlnes, better to assgn the hgher prorty to the task wth the shorter perod 1973 Lu & Layland Rate-Monotonc prorty orderng s optmal for mplct deadlne perodc tasksets (synchronous arrvals) 1982 Leung & Whtehead Deadlne-Monotonc prorty orderng s optmal for constraned deadlne tasksets (synchronous arrvals) Deadlne Monotonc not optmal for the asynchronous case (offsets) 1990 Lehoczky Deadlne Monotonc not optmal for arbtrary deadlne tasksets 1994 Burns et al. Deadlne Monotonc not optmal for deadlnes pror to completon 1996 George Deadlne Monotonc not optmal for non-pre-emptve schedulng 9

10 Deadlne Monotonc: non-optmalty Tasks wth offsets Task Executon Tme Deadlne Perod Offset A B [J.Y.-T. Leung, J. Whtehead "On the complexty of fxed-prorty schedulng of perodc real-tme tasks, Performance Evaluaton, 2(4): , 1982] 10

11 Deadlne Monotonc: non-optmalty Tasks wth arbtrary deadlnes Task Executon Tme Deadlne Perod A B [Lehoczky J., Fxed prorty schedulng of perodc task sets wth arbtrary deadlnes. In proceedngs Real-Tme Systems Symposum, pages , 1990] 11

12 Deadlne Monotonc: non-optmalty Tasks wth deadlnes pror to completon Task Executon Tme Deadlne Perod A B [A. Burns, K. Tndell, A.J. Wellngs, "Fxed prorty schedulng wth deadlnes pror to completon" In proceedngs of the sxth Euromcro Workshop on Real-Tme Systems. pp , 1994] 12

13 Deadlne Monotonc: non-optmalty Non-pre-emptve schedulng Task Executon Tme Deadlne Perod A B C [L. George, N. Rverre, M. Spur, Preemptve and Non-Preemptve Real-Tme UnProcessor Schedulng, INRIA Research Report, No. 2966, September 1996] Example derved from: [R.I. Davs and A. Burns "Robust prorty assgnment for messages on Controller Area Network (CAN). Real-Tme Systems, Volume 41, Issue 2, pages , February 2009] 13

14 Optmal Prorty Assgnment for each prorty level, lowest frst { for each unassgned task τ { f τ s schedulable at prorty assumng that all unassgned tasks are at hgher prortes { assgn task τ to prorty level break (ext for loop) } } f no tasks are schedulable at prorty { return unschedulable } } return schedulable n(n+1)/2 schedulablty tests rather than n! by explorng all possble orderngs n = 25, that s 325 tests rather than Tasks A, A, B, A, A, B, A C, C, D, E E E [N.C. Audsley, "Optmal prorty assgnment and feasblty of statc prorty tasks wth arbtrary start tmes", Techncal Report YCS 164, Dept. Computer Scence, Unversty of York, UK, 1991.] [N.C. Audsley, On prorty assgnment n fxed prorty schedulng, Informaton Processng Letters, 79(1): 39-44, May 2001.] [K. Bletsas, and N.C. Audsley, Optmal prorty assgnment n the presence of blockng. Informaton Processng 14 Letters Vol. 99, No. 3, pp83-86, August. 2006] A C E B D

15 OPA algorthm applcablty Powerful dea as we have sad very lttle about the actual schedulablty test hence broad applcablty OPA algorthm provdes optmal prorty assgnment w.r.t. any schedulablty test S for fxed prorty schedulng provded that three condtons are met Condton 1: Schedulablty of a task may, accordng to the test, be dependent on the set of hgher prorty tasks, but not on ther relatve prorty orderng Condton 2: Schedulablty of a task may, accordng to the test, be dependent on the set of lower prorty tasks, but not on ther relatve prorty orderng Condton 3: When the prortes of any two tasks of adjacent prorty are swapped, the task beng assgned the hgher prorty cannot become unschedulable accordng to the test, f t was prevously deemed schedulable at the lower prorty Tests meetng these condtons referred to as OPA-compatble [R.I. Davs, A. Burns "Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. In proceedngs Real-Tme Systems Symposum pp , 2009.] 15

16 Multprocessor: global FP schedulng Global FP schedulng Sngle global run-queue fxed prorty pre-emptve schedulng on multple processsors Incompatble wth OPA Any exact test (B. Andersson and Jonsson 2000) such as those for perodc tasksets gven by Cucu and Goossens (2006, 2007). Response tme analyss (RTA test) of Bertogna and Crne (2007) Improved RTA test of Guan et al. (2009) Compatble wth OPA Deadlne Analyss (DA test) of Bertogna et al. (2009) Smple Response Tme test of B. Andersson and Jonsson (2001) [R.I. Davs and A. Burns "Improved Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. Real-Tme Systems, Vol. 47, No. 1, pp.1-40, 2011.] 16

17 Global FP schedulablty tests #1 Deadlne Analyss DA test (Bertogna et al. 2009) + ) ( ) ( 1 k hp k D k k D I m C D 1) ), ( mn( ) ( + = k k k D k D C D D W D I ) ) (, mn( ) ( ) ( k k k k D T D N C D D C C D N D W + + = + = k k T C D D D N ) ( C T D D k Compatble wth OPA

18 Global FP schedulablty tests #2 Response Tme Analyss RTA test (Bertogna & Crne 2007) T R C R UB k C I W k 1 + m I hp( k) R UB k ( R UB k ) UB R UB UB ( Rk ) = mn( W ( Rk ), Rk Ck + 1) R R UB R ( L) = N ( L) C + mn( C, L + R C N ( L) T UB L + R C R N ( L) = T Incompatble wth OPA )

19 Multprocessor: global FP schedulng RTA test domnates DA test Whch s better? RTA test + heurstc prorty assgnment Deadlne Monotonc D C Monotonc DkC Monotonc (k s a factor that depends on the number of processors) DA test + Optmal prorty assgnment [R.I. Davs and A. Burns "Improved Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. Real-Tme Systems, Vol. 47, No. 1, pp.1-40, 2011.] 19

20 Global FP: Prorty Assgnment 120% Percentage of tasksets schedulable 100% 80% 60% 40% 20% DA (OPA) RTA (DKC) DA (DKC) RTA (DCMPO) DA (DCMPO) RTA (DMPO) DA (DMPO) 4 Processors 20 tasks 0% Utlsaton 20

21 Global FP: Prorty Assgnment 120% Percentage of tasksets schedulable 100% 80% 60% 40% 20% DA (OPA) RTA (DKC) DA (DKC) RTA (DCMPO) DA (DCMPO) RTA (DMPO) DA (DMPO) 8 Processors 40 tasks 0% Utlsaton 21

22 Global FP: Prorty Assgnment 120% Percentage of tasksets schedulable 100% 80% 60% 40% 20% DA (OPA) RTA (DKC) DA (DKC) RTA (DCMPO) DA (DCMPO) RTA (DMPO) DA (DMPO) 16 Processors 80 tasks 0% Utlsaton 22

23 Beyond OPA What to do f the schedulablty test s not OPA-compatble (e.g. RTA test for global FP schedulng)? Search n! combnatons? How to prune the search space? Use domnance relatonshp between tests OPA-compatble Necessary condton C-RTA Domnates OPA-ncompatble RTA test Domnates OPA-compatble Suffcent test DA test Use the suffcent test and the necessary condton to prune the choce of tasks at each prorty level [R.I. Davs and A. Burns, On Optmal Prorty Assgnment for Response Tme Analyss of Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Hard Real-Tme Systems. Unversty of York, Department of Computer Scence Techncal Report, YCS , Aprl 2010.] 23

24 + = R T C C L L N ) ( ) ) (, mn( ) ( ) ( R R R T L N C C L C C L N L W + + = C-RTA necessary test Based on Response Tme Analyss RTA test (Bertogna & Crne 2007) + ) ( ) ( 1 k hp UB k k UB k R I m C R 1) ), ( mn( ) ( + = k UB k UB k R UB k C R R W R I ) ) (, mn( ) ( ) ( R UB R R T L N C R L C C L N L W + + = + = UB R T C R L L N ) ( C T R R UB k C T C R UB k

25 Search wth backtrackng OPA-Compatble Suffcent test mples schedulable OPA-Compatble Necessary test mples unschedulable [R.I. Davs and A. Burns, On Optmal Prorty Assgnment for Response Tme Analyss of Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Hard Real-Tme Systems. Unversty of York, Department of Computer Scence Techncal Report, YCS , Aprl 2010.] 25

26 Percentage of tasksets schedulable 120% 100% 80% 60% 40% 20% 0% Global FP: Prorty Assgnment Utlsaton C-RTA (OPA) RTA(OPA-Heurstc) DA-LC (OPA) 8 Processors 40 tasks [R.I. Davs and A. Burns, On Optmal Prorty Assgnment for Response Tme Analyss of Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Hard Real-Tme Systems. Unversty of York, Department of Computer Scence Techncal Report, YCS , Aprl 2010.] 26

27 Mnmsng the number of Prorty Levels wth OPA Important for practcal systems that may support only a lmted number of prortes for each prorty level, lowest frst { Z = empty set for each unassgned task τ { f τ s schedulable at prorty assumng that all unassgned tasks are at hgher prortes { add τ to Z } } f no tasks are schedulable at prorty { return unschedulable } else { assgn all tasks n Z to prorty } f no unassgned tasks reman { break } } return schedulable [N.C. Audsley, On prorty assgnment n fxed prorty schedulng, Informaton Processng Letters, 79(1): 39-44, May 2001.] 27

28 Intermsson 28

29 Robust Prorty Assgnment Drawback of OPA algorthm Arbtrary choce of schedulable tasks at each prorty May leave the system only just schedulable.e fragle not robust to mnor changes In practce tasks may be subject to addtonal nterference Executon tme budget overruns; nterrupts occurrng n bursts or at ll-defned rates; ll-defned RTOS overheads; ll-defned crtcal sectons; cycle stealng by perpheral devces (DMA) etc. etc. Want a robust prorty orderng, able to tolerate the maxmum amount of addtonal nterference [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 29

30 Addtonal Interference Very general model of addtonal nterference Addtonal Interference functon E(α,w,) α scalng factor used to model varablty w tme wndow over whch nterference occurs prorty level at or below whch the nterference mpnges on task response tmes Requre that E(α,w,) s a monotonc non-decreasng functon of ts parameters In practce most sources of nterference are Greater n longer ntervals of tme than n shorter ones Affect lower prortes f they also affect hgher prortes Guaranteed to be monotonc n α as ths s the scalng factor [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 30

31 Robust Prorty Assgnment Defnton: Robust Prorty Assgnment (wth an addtonal nterference functon E(α,w,) ) For a gven system model and addtonal nterference functon, a prorty assgnment polcy P s referred to as robust f there are no systems, complant wth the system model, that are schedulable and can tolerate addtonal nterference characterzed by a scalng factor α usng another prorty assgnment polcy Q that are not also schedulable and can tolerate addtonal nterference characterzed by the same or larger scalng factor usng prorty assgnment polcy P. Of all feasble prorty assgnments, the robust prorty assgnment tolerates the most addtonal nterference (largest α) [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 31

32 Robust Prorty Assgnment (RPA) algorthm Based on OPA algorthm Same three condtons needed for compatblty Condton 1: Schedulablty of a task may, accordng to the test, be dependent on the set of hgher prorty tasks, but not on ther relatve prorty orderng Condton 2: Schedulablty of a task may, accordng to the test, be dependent on the set of lower prorty tasks, but not on ther relatve prorty orderng Condton 3: When the prortes of any two tasks of adjacent prorty are swapped, the task beng assgned the hgher prorty cannot become unschedulable accordng to the test, f t was prevously deemed schedulable at the lower prorty As addtonal nterference E(α,w,) s monotoncally non-decreasng n ts parameters, the above condtons also hold when addtonal nterference s consdered [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 32

33 RPA Algorthm for each prorty level, lowest frst { for each unassgned task τ { determne the largest value of α for whch task τ s schedulable at prorty assumng that all unassgned tasks have hgher prortes } f no tasks are schedulable at prorty { return unschedulable } else { assgn the schedulable task that tolerates the max α at prorty to prorty } } return schedulable 33

34 Robust Prorty Assgnment Example 1: Non-pre-emptve schedulng Addtonal nterference from sngle nvocaton of an nterrupt handler wth unknown executon tme Addtonal nterference E( α, w, ) = α Task C D T τ A τ B τ C τ D τ E

35 Robust Prorty Assgnment Computed values of α Prorty Task τ A τ B τ C τ D τ E 5 NS NS NS NS NS NS Robust prorty orderng Tolerates addtonal nterference of up to 110 tme unts Deadlne monotonc: nether optmal nor robust Tolerates addtonal nterference of up to 74 tme unts OPA: may be worse stll Mght tolerate addtonal nterference of only 10 tme unts 35

36 Robust Prorty Assgnment Example 2: Pre-emptve schedulng, D >T Task C D T τ A τ B Schedulable wth prorty orderngs (τ A,τ B ) and (τ B,τ A ) wth no addtonal nterference 36

37 Robust Prorty Assgnment Case 1: (τ A,τ B ) tolerates α = (58, 9) (τ B,τ A ) tolerates α = (51, 10) Robust orderng Case 2: w E( α, w, ) = α 100 w E( α, w, ) = α 200 (τ A,τ B ) tolerates α = (76, 18) Robust orderng (τ B,τ A ) tolerates α = (96, 15) Case 3: w w E( α, w, ) = α K + L Robust orderng depends on specfc values of K and L K=1, L=0: equvalent to Case 1: (τ B,τ A ) s the Robust orderng K=0, L=1: equvalent to Case 2: (τ A,τ B ) s the Robust orderng 37

38 Robust Prorty Assgnment Result #1 (somewhat negatve) In general, a Robust prorty orderng can only be found f the form of the addtonal nterference functon s well defned (only α unknown). Often t can be well defned e.g. robust to maxmum amount of addtonal nterference at the hghest prorty level, maxmum number of transmsson faults etc. But more to follow on specfc system models [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 38

39 Robust Prorty Assgnment Mxed systems: two subsets of tasks DM tasks Satsfy the restrctons where Deadlne Monotonc prorty orderng s known to be optmal Pre-emptable, D T, resource access accordng to SRP, no transactons or offsets Non DM tasks Don t satsfy the restrctons where Deadlne Monotonc prorty orderng s known to be optmal Pre-emptable wth D>T, non-pre-emptable, co-operatve schedulng wth non-pre-emtable fnal sectons, transactons, non-zero offset [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 39

40 Robust Prorty Assgnment Result #2 For systems contanng only DM tasks, Deadlne Monotonc prorty orderng s optmal and also robust, rrespectve of task executon tmes and rrespectve of the form of the addtonal nterference E(α,w,) provded only that the addtonal nterference s monotonc n ts parameters. Result #3 For mxed systems contanng both DM and non DM tasks, then there exsts a robust prorty order wth the DM tasks n Deadlne Monotonc partal order* *Ths holds provded that the nterference from non DM tasks s monotoncally nondecreasng w.r.t. tme ntervals and prorty levels, and not dependent on specfc tasks [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 40

41 Robust Prorty Assgnment DM task (e.g. constraned deadlne) Non DM task (e.g. arbtrary deadlne, part of a transacton etc.) Prorty Deadlne Monotonc Partal order 41

42 Robust Prorty Assgnment Can mprove effcency of OPA and RPA algorthms Of all the DM tasks, the one wth the largest deadlne s the one that can tolerate the most addtonal nterference at a gven prorty level Only one DM task need be checked at each prorty level the one wth the largest deadlne of all unassgned DM tasks For n tasks, k of whch are DM tasks: (n(n+1)-k(k-1))/2 task schedulablty tests nstead of n(n+1)/2 Example: 4 tasks n a transacton, 46 ndependent tasks max. of 240 schedulablty tests nstead of 1275 [R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December 2007.] 42

43 Mxed Crtcalty Examples Aerospace: e.g. UAVs Automotve: ASILs e.g. cruse control v. electronc steerng assstance Task Model Tasks have dfferent crtcalty levels (e.g. HI and LO) HI crtcalty tasks have dfferent executon tme bounds for the two crtcalty levels: C HI and C LO When a HI task exceeds ts LO crtcalty executon budget, then the system enters HI crtcalty mode In HI crtcalty mode, all HI crtcalty tasks must meet ther deadlnes assumng HI crtcalty executon tmes, LO crtcalty tasks may be abandoned In LO crtcalty mode, all tasks must meet ther deadlnes assumng LO crtcalty executon tmes [S.K. Baruah, A. Burns, R.I. Davs Response Tme Analyss for Mxed Crtcalty Systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages 34-43, Nov 29th - Dec 2nd, 2011] 43

44 Mxed Crtcalty FP Schedulng AMC-rtb LO crtcalty mode: R LO = C ( LO) + HI crtcalty mode: R = R Hgh Low crtcalty tasks R T C E(α,w,) j j hph ( ) j ( LO) + R T C E(α,w,) k k hpl( ) k ( LO) R = C ( HI) + j hph ( ) R T j C j ( HI) + k hpl( ) R T LO k C E(α,w,) k ( LO) [S.K. Baruah, A. Burns, R.I. Davs Response Tme Analyss for Mxed Crtcalty Systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages 34-43, Nov 29th - Dec 2nd, 2011] 44

45 Mxed Crtcalty FP Schedulng LO Crtcalty tasks HI Crtcalty tasks DM Prorty order DM Prorty order 2n-1 schedulablty tests rather than n(n+1)/2 [S.K. Baruah, A. Burns, R.I. Davs Response Tme Analyss for Mxed Crtcalty Systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages 34-43, Nov 29th - Dec 2nd, 2011] 45

46 Prorty assgnment n probablstc real-tme systems Tasks wth executon tmes modelled as ndependent random varables Task Executon Tme Deadlne Perod DMR threshold A B Deadlne monotonc prorty orderng not optmal Task A at hgher prorty P(R A > D A )=0 P(R B > D B )=0.06 Task B at hgher prorty P(R B > D B )=0 P(R A > D A )=0.44 [D. Maxm, O. Buffet, L. Santnell, L. Cucu-Grosjean, R. I. Davs Optmal Prorty Assgnment Algorthms for Probablstc Real-Tme Systems. In proceedngs 19th Internatonal Conference on Real-Tme and Network Systems (RTNS'11), Sept 29-30th, 2011.] 46

47 Optmal Prorty Assgnment for probablstc systems Same three condtons needed for OPA compatblty Condton 1: Schedulablty of a task may, accordng to the test, be dependent on the set of hgher prorty tasks, but not on ther relatve prorty orderng Condton 2: Schedulablty of a task may, accordng to the test, be dependent on the set of lower prorty tasks, but not on ther relatve prorty orderng Condton 3: When the prortes of any two tasks of adjacent prorty are swapped, the task beng assgned the hgher prorty cannot become unschedulable accordng to the test, f t was prevously deemed schedulable at the lower prorty Defnton of schedulable very dfferent based on probablty of deadlne falure (.e. response tme dstrbuton and ts exceedance functon) compared to Dead Mss Rato threshold 47

48 RTSS 2012 Please come along to my talk at 11:30am on 5 th Dec 2012 RTSS 2012 San Juan, Puerto Rco Optmal Fxed Prorty Schedulng wth Deferred Pre-empton Rob Davs and Marko Bertogna 48

49 Interestng problems not obvously amenable to OPA FPDS: Mnmsng the number of pre-emptons through maxmsng blockng (Bertogna et al 2011) Can be done from hghest prorty down rather than lowest prorty up, but then requres a pre-defned prorty orderng Probablstc: Mnmsng average/total probablty of deadlne falure across all tasks (Maxm et al 2011) Swappng tasks at adjacent prortes may decrease the total, even f the larger of the two probabltes of deadlne falure decreases NoC wormhole communcaton: Assgnng prortes to network flows (Sh and Burns, 2008) Response tme of a network flow depends on the response tmes of hgher prorty flows Pre-empton thresholds: Assgnment of base prortes and preempton thresholds (Wang and Saksena, 1999) Pre-empton threshold assgnment depends on the relatve prorty orderng of hgher prorty tasks 49

50 Interestng problems not obvously amenable to OPA Cache Related Pre-empton Delays (CRPD) Response tmes depend upon the relatve prorty orderng of hgher prorty tasks CRPD [S. Altmeyer, R.I. Davs, C. Maza Improved cache related pre-empton delay aware response tme analyss for fxed prorty pre-emptve systems. Real-Tme Systems, Volume 48, Issue 5, Pages , Sept 2012.] [S. Altmeyer, R.I. Davs, C. Maza Cache related pre-empton delay aware response tme analyss for fxed prorty pre-emptve systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages , Nov 50 29th - Dec 2nd, 2011]

51 Questons? 51

52 References S. Altmeyer, R.I. Davs, C. Maza Improved cache related pre-empton delay aware response tme analyss for fxed prorty pre-emptve systems. Real-Tme Systems, Volume 48, Issue 5, Pages , Sept S. Altmeyer, R.I. Davs, C. Maza Cache related pre-empton delay aware response tme analyss for fxed prorty pre-emptve systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages , Nov 29th - Dec 2nd, N.C. Audsley, "Optmal prorty assgnment and feasblty of statc prorty tasks wth arbtrary start tmes", Techncal Report YCS 164, Dept. Computer Scence, Unversty of York, UK, N.C. Audsley, On prorty assgnment n fxed prorty schedulng, Informaton Processng Letters, 79(1): 39-44, May S.K. Baruah, A. Burns, R.I. Davs Response Tme Analyss for Mxed Crtcalty Systems. In proceedngs 32nd IEEE Real-Tme Systems Symposum (RTSS'11), pages 34-43, Nov 29th - Dec 2nd, M. Bertogna, G. Buttazzo, G. Yao. "Improvng Feasblty of Fxed Prorty Tasks usng Non- Preemptve Regons", In Proceedngs Real-Tme Systems Symposum, Venna, Austra, December K Bletsas, N Audsley, Optmal prorty assgnment n the presence of blockng Informaton processng letters 99 (3), 83-86, A. Burns, K. Tndell, A.J. Wellngs, "Fxed prorty schedulng wth deadlnes pror to completon" In proceedngs of the sxth Euromcro Workshop on Real-Tme Systems. pp , A. Burns, Dual Prorty Schedulng: Is the Processor Utlsaton bound 100% In proceedngs RTSOPS,

53 References R.I. Davs and A. Burns, Optmal Prorty Assgnment for Aperodc Tasks wth Frm Deadlnes n Fxed Prorty Pre-emptve Systems. Informaton Processng Letters 53(5). 10 th March R.I. Davs, A. Burns. "Robust Prorty Assgnment for Fxed Prorty Real-Tme Systems. In proceedngs IEEE Real-Tme Systems Symposum pp Tucson, Arzona, USA. December R.I. Davs, A. Burns "Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. In proceedngs Real-Tme Systems Symposum pp , R.I. Davs and A. Burns "Robust prorty assgnment for messages on Controller Area Network (CAN). Real-Tme Systems, Volume 41, Issue 2, pages , February R.I. Davs and A. Burns, On Optmal Prorty Assgnment for Response Tme Analyss of Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Hard Real-Tme Systems. Unversty of York, Department of Computer Scence Techncal Report, YCS , Aprl R.I. Davs and A. Burns "Improved Prorty Assgnment for Global Fxed Prorty Pre-emptve Schedulng n Multprocessor Real-Tme Systems. Real-Tme Systems, Vol. 47, No. 1, pp.1-40, R.I. Davs, S. Kollmann, V. Pollex, F. Slomka, "Schedulablty Analyss for Controller Area Network (CAN) wth FIFO Queues Prorty Queues and Gateways. Real-Tme Systems, R.I. Davs, M. Bertogna "Optmal Fxed Prorty Schedulng wth Deferred Pre-empton. In proceedngs 33rd IEEE Real-Tme Systems Symposum (RTSS'12), Dec 4th - 7th,

54 References M.S. Fneberg and O. Serln, Multprogrammng for hybrd computaton, In proceedngs AFIPS Fall Jont Computng Conference, pp 1-13, 1967 George, L., Rverre, N., Spur, M., Preemptve and Non-Preemptve Real-Tme UnProcessor Schedulng, INRIA Research Report, No. 2966, September Lehoczky J., Fxed prorty schedulng of perodc task sets wth arbtrary deadlnes. In Proceedngs Real-Tme Systems Symposum, pp , J.Y.-T. Leung, J. Whtehead "On the complexty of fxed-prorty schedulng of perodc real-tme tasks, Performance Evaluaton, 2(4): , Lu C.L., Layland J.W., "Schedulng algorthms for multprogrammng n a hard-real-tme envronment", Journal of the ACM, 20(1) pp 46-61, D. Maxm, O. Buffet, L. Santnell, L. Cucu-Grosjean, R. I. Davs Optmal Prorty Assgnment Algorthms for Probablstc Real-Tme Systems. In proceedngs 19th Internatonal Conference on Real-Tme and Network Systems (RTNS'11), Sept 29-30th, S. Vestal. Preemptve schedulng of mult-crtcalty systems wth varyng degrees of executon tme assurance. In Proceedngs of the Real-Tme Systems Symposum, pp , Y. Wang and M. Saksena. Schedulng fxed-prorty tasks wth pre-empton threshold. In Proceedngs RTCSA 99, Hong Kong, Chna, December 13-15, S. Zheng, A. Burns, Prorty Assgnment for Real-Tme Wormhole Communcaton n On-Chp Networks. In Proceedngs Real-Tme Systems Symposum, pp , A. Zuhly and A. Burns, Optmalty of (D-J)-monotonc prorty assgnment. Informaton Processng Letters, Vol. 103 No. 6,

55 References A. Zuhly, A. Burns: Exact schedulng analyss of non-accumulatvely monotonc multframe tasks. Real-Tme Systems 43(2): (2009) 55