EDF Scheduling for Identical Multiprocessor Systems

Transcription

1 EDF Schedulng for dentcal Multprocessor Systems Maro Bertogna Unversty of Modena, taly

2 As Moore s law goes on Number of transstor/chp doubles every 18 to 24 mm

3 heatng becomes a problem Power densty (W/cm 2 ) Pentum P1 P Pentum Tejas cancelled! P3 P4 Nuclear Reactor STOP!!! Hot-plate Power 0, Year P V f: Cloc speed lmted to less than 4 GHz

4 Technology trends Reduced gate szes Hgher frequences allowed Larger number of transstors BUT Physcal lmts of semconductor-based mcroelectroncs Larger dynamc power consumed Leaage current becomes mportant Hgher densty of transstors

5 ntel s tmelne Year Processor Manufacturng Number of Frequency Technology transstors µm 108 Hz µm 800 Hz µm 2 MHz µm 5 MHz µm 5 MHz ,5 µm 6 MHz ,5 µm 16 MHz µm 25 MHz Pentum 0,8 µm 66 MHz Pentum Pro 0,6 µm 200 MHz Pentum 0,25 µm 300 MHz Pentum 0,18 µm 500 MHz Pentum 4 0,18 µm 1,5 GHz Pentum M 90 nm 1,7 GHz Pentum D 65 nm 3,2 GHz Core 2 Duo 65 nm 2,93 GHz Core 2 Quad 65 nm 2,66 GHz Core 2 Quad X 45 nm 3 GHz Core 3, 5, 7 32 nm 3,33 GHz Core 5, 7 22 nm 3,4 GHz ? 16nm?

6 Power, frequency and voltage P = A C V 2 f + V lea Dynamc power Statc power (mportant below 100nm) There s no way out for classc frequency scalng on sngle cores systems!

7 Keepng Moore s law alve Explot the mmense number of transstors n other ways Reduce gate szes mantanng the frequency suffcently low Use a hgher number of slower logc gates n other words: Swtch to Multcore Systems!

8 How many cores n the future? Patterson & Hennessy: number of cores wll double every 18 months, whle power, cloc frequency and costs wll reman constant More lely to be applcaton dependent Many trade-offs Technology lmts Transstor densty Amdahl s law

9 Amdahl s law The total speedup that can be obtaned ncreasng the number of processors s Parallel porton of applcaton Number of processors/cores

10 Amdahl s law The total speedup that can be obtaned ncreasng the number of processors s n practce, performance/prce falls rapdly as Ns ncreased, even wth a small (1 P) E.g.: P = 90% (1 P) = 10% speedup < 10

11 Amdahl s law

12 Consequences Parallel computng s lely to be useful for Small/medum number of processors, or Embarrassngly parallel problems(p 1) Large number of parallel tass wth no dependences E.g., brute-force search n cryptography, 3D projecton, GPU handled problems, etc. 1 4 GHz = 2 2 GHz Memory, bus and /O bottlenecs mpose further constrants

13 Real-tme schedulablty on dentcal multprocessor systems

14 System model Platform wth m dentcal processors Tas set τwth nndependent sporadctass τ Perod or mnmum nter-arrval tme T Worst-case executon tme C Deadlne D Utlzaton U =C /T, densty λ =C /mn(d,t )

15 Possble problems Feasblty problem Run-tme schedulng problem Schedulablty problem τ 3 τ 1 τ 2? CPU1 CPU2 τ 5 τ 4 CPU3 w.r.t. a gven tas model

16 Unprocessor RT Systems Sold theory (startng from the 70s) Optmal schedulers Tght schedulablty tests for dfferent tas models Shared resource protocols Bandwdth reservaton schemes Herarchcal schedulers RTOS support

17 Sngle processor EDF Optmal f a set of jobs s feasble, than t can be successfully scheduled wth EDF Bounded number of preemptons Effcent mplementatons Exact feasblty condtons Lnear test for mplct deadlnes: U tot 1 Pseudo-polynomal test for constraned and arbtrary deadlnes [Baruah et al. 90]

18 Mulprocessors are dffcult The smple fact that a tas can use only one processor even when several processors are free at the same tme adds a surprsng amount of dffculty to the schedulng of multple processors [Lu 69] CPU1 CPU2 CPU3

19 Multprocessor RT Systems Many NP-hard problems Few optmalty results Heurstc approaches Smplfed tas models Only suffcent schedulablty tests Lmted RTOS support

20 Global vs parttoned schedulng Sngle system-wde queue nstead of multple per-processor queues: Global schedulng Parttoned approach CPU1 τ 1 τ 5 τ 4 τ 1 CPU1 τ 1 τ 5 τ 4 τ 3 τ 2 τ 1 CPU2 τ 2 τ 3 τ 2 CPU2 τ 2 CPU3 τ 3 CPU3

21 Parttoned schedulng The schedulng problem reduces to: Bn-pacng problem NP-hard n the strong sense + Unprocessor schedulng problem Well nown τ 1 τ 3 τ 5 τ 2 τ 4 Varous heurstcs used: FF, NF, BF, FFDU, BFDD, etc. EDF U tot 1 RM (RTA)...

22 Parttoned schedulablty [Lopez et al.] EDF-FF gves the best utlzaton bound among all possble parttonng methods: A refned bound, when U max s the maxmum utlzaton among all tass, s:

23 Parttoned schedulablty m

24 Global schedulng The m hghest prorty ready jobs are always scheduled Wor-conservng scheduler No processor s ever dled when a tas s ready to execute. CPU1 τ 1 τ 5 τ 4 τ 3 τ 2 τ 1 CPU2 τ 2 CPU3 τ 3

25 Global schedulng propertes Load automatcally balanced Easer re-schedulng (dynamc loads, selectve shutdown, etc.) Lower average response tme (see queueng theory) More effcent reclamng and overload management Smaller number of preemptons Mgraton cost: can be mtgated by proper HW (e.g., MPCore s Drect Data nterventon) Few schedulablty tests Further research needed o Global and parttoned approaches are ncomparable

26 Global schedulng problem Optmal algorthms (U tot m) are nown only for mplct deadlne systems: PFar (PF, PD, PD 2 ), Boundary-Far (DP-Wrap, LLREF, BF, ), EKG, RUN, U-EDF [ECRTS 12] Preempton and synchronzaton ssues No optmal scheduler nown for more general tas models Classc schedulers (e.g., EDF) are not optmal Dhall s effect

27 Dhall s effect Example: mprocessors, n=m+1tass, D = T τ 1,, τ m = (1,T-1) τ m+1 = (T,T) m lght tass 1 heavy tas U tot 1 DEADLNE MSS EDF can fal at very low utlzatons T

28 Beyond mplct deadlnes No optmal algorthm s nown for constraned or arbtrary deadlne systems No optmal on-lnealgorthm s possble for arbtrary collecton of jobs [Leung and Whtehead] Optmal algorthms for sporadc tas system wth constraned deadlnesrequre clarvoyance[fsher et al 09]

29 Global EDF schedulng Smplemplementaton ntutve prorty assgnment Reduced schedulng overhead Small number of preemptons/mgratons Bounded tardness(as long as U tot m) Good performance on average Many suffcentschedulablty tests But most of them are far from tghtness Exact tests are ntractable

30 Global EDF: man results Many suffcent schedulablty tests: GFB (RTSJ 01) BAK (RTSS 03 TPDS 05) BAR (RTSS 07) LOAD (ECRTS 07,ECRTS 08,RTSJ 08 RTSJ 09) BCL (ECRTS 05 TPDS 09) RTA (RTSS 07) FF-DBF (ECRTS 09) Most tests are ncomparable

31 Crtcal nstant A partcular confguraton of releases that leads to the largest possble response tme of a tas. Possble to derve exact schedulablty tests analyzng just the crtcal nstant stuaton. Unprocessor FP and EDF: a crtcal nstant s when all tass arrve synchronously all jobs are released as soon as permtted

32 Multprocessor anomaly Synchronous perodc arrval of tass s not a crtcal nstant for multprocessors: τ 1 = (1,1,2) τ 2 = (1,1,3) τ 3 = (5,6,6) Synchronous Second job perodc of τ 2 delayed stuaton by one unt from [Bar07] Need to fnd pessmstc stuatons to derve suffcent schedulablty tests

33 Problem wndow L Frst mssed deadlne τ D t T C τ ε D C Carry-n

34 Adopted technques Consder the nterference on the problem job Bound the nterference wth the worload Use an upper bound on the worload Exstng schedulablty tests dffer n Problem wndow selecton: L Carry-n bound ε n the consdered wndow Amount of each contrbuton (BAK, LOAD, BCL, RTA) Number of carry-n contrbutons (BAR, LOAD) Total amount of all contrbutons (FF-DBF, GFB)

35 ntroducng the nterference = Total nterference suffered by tas τ = nterference of tas τ on tas τ CPU3 CPU2 CPU τ τ τ r r +R R ( R = ( R ) m ) 1 = C + = + ( R ) C m ( R )

36 Lmtng the nterference t s suffcent to consder at most the porton (R -C +1) of each term n the sum CPU3 CPU2 CPU1 r τ τ τ r +R ( R ) ( R ) < R C + 1 t can be proved that WCRT s gven by the fxed pont of: R C 1 + m mn( ( R ), R C + 1)

37 Boundng the nterference Exactly computng the nterference s complex Pessmstc assumptons: 1. Bound the nterference of a tas wth the worload: ( R ) W ( R 2. Use an upper bound on the worload. )

38 Boundng the worload Consder a stuaton n whch: The frst job executes as close as possble to ts deadlne Successve jobs execute as soon as possble D T ε τ where: W C C C C ( L) w ( L) = N ( L) C + ε ( L) L L + D C N ( L) = T ε ( L) = mn( C, L + D C N ( L) T ) (# jobs excluded the last one) (last job)

39 Boundng the worload Consder a stuaton n whch: The frst job executes as close as possble to ts deadlne Successve jobs execute as soon as possble D T ε τ C C C C L An upper bound on the WCRT of tas s gven by the fxed pont of R n the teraton: R C + 1 m mn( w ( R ), R C + 1)

40 nterference refnement The computed bound R can be used to mprove the nterference estmaton where: + = T C R L R L N ), ( ) ), (, mn( ), ( T R L N C R L C R L + = ε C τ L D C C C T R ), ( ), ( ), ( ) ( R L C R L N R L w L W ε + =

41 teratve schedulablty test 1. All response tmes R ntalzed to D 2. Compute response tme bound for tass 1,,n f smaller than old value update R f R > D, mar as temporarly not schedulable 3. f all tass have R D return success 4. f no response tme has been updated for tass 1,,n return fal 5. Otherwse, return to pont 2

42 Consderatons Very good performances Allows fndng the largest number of EDF schedulable tas sets for varous load dstrbutons Pseudo-polynomal complexty A smpler verson taes O(n 2 ) Fast average behavor

43 Conclusons Real-Tme systems need to deal wth the multcore revoluton Multprocessor Real-Tme systems are dffcult No crtcal nstant Optmalty often needs clarvoyance Many suffcent schedulablty tests Often far from tght condtons Exact tests are ntractable Further research s needed!

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