Priority-Driven Scheduling of Periodic Tasks. Why Focus on Uniprocessor Scheduling?

Transcription

1 CPSC-663: Ra-m Systms Prorty-Drv Schdu Prorty-Drv Schdu of Prodc ass Prorty-drv vs. coc-drv schdu: coc-drv: cycc schdu xcutv rocssor tass a ror! rorty-drv: tass rorty quu rocssor Assumtos: tass ar rodc jobs ar rady as soo as thy ar rasd rmto s aowd tass ar ddd o arodc or soradc tass W w atr: trat arodc ad soradc tass trat rsourcs tc. Why Focus o Urocssor Schdu? Dyamc vs. statc mutrocssor schdu: Dyamc : tass Statc : tass tas assmt rorty quu art art art3 art4 rocssors oca rorty quus Poor worst-cas rformac of rorty-drv aorthms dyamc vromts. Dffcuty vadat tm costrats.

2 CPSC-663: Ra-m Systms Prorty-Drv Schdu Statc-Prorty vs. Dyamc Prorty Statc-Prorty: A jobs tas hav sam rorty. xam: Rat-Mootoc: h shortr th rod, th hhr th rorty. 5, 3, 5 3,, 3 Dyamc-Prorty: May ass dffrt rorts to dvdua jobs. xam: Earst-Dad-Frst: h arr th absout dad, th hhr th rorty. hr w bra t s ot rmtd Exam Aorthms Statc-Prorty: Rat-Mootoc RM: h shortr th rod, th hhr th rorty. [LuLayad 73] Dad-Mootoc DM: h shortr th ratv dad, th hhr th rorty. [LuWhthad 8] For arbtrary ratv dads, DM outrforms RM. Dyamc-Prorty: EDF: Earst-Dad-Frst. LS: Last-Sac-m-Frst. FIFO/LIFO tc.

3 CPSC-663: Ra-m Systms Prorty-Drv Schdu Cosdratos about Prorty-Drv Schdu FIFO/LIFO do ot ta to accout urcy of jobs. Statc-rorty assmts basd o fuctoa crtcaty ar tycay ootma. W cof our attto to aorthms that ass rorts basd o tmora aramtrs. Df: [Schduab Utzato] Evry st of rodc tass wth tota utzato ss or qua tha th schduab utzato of a aorthm ca b fasby schdud by that aorthm. h hhr th schduab utzato, th bttr th aorthm. Schduab utzato s aways ss or qua.0! Schduab Utzato of FIFO Rsut of Oo Po CPSC-663 of Fa 00: Numbr of Vots 0% % 0% 30% 40% 50% 00% 3

4 CPSC-663: Ra-m Systms Prorty-Drv Schdu Schduab Utzato of FIFO II horm: U FIFO 0 Proof: Gv ay utzato v ε > 0, w ca fd a tas st, wth utzato ε, whch may ot b fasby schdud accord to FIFO. Exam tas st: : : ε U ε ε Otmaty of EDF for Prodc Systms horm: A systm of ddt rmtab tass wth ratv dads qua to thr rods s fasb ff thr tota utzato s ss or qua. Proof: oy-f: obvous f : fd aorthm that roducs fasb schdu of ay systm wth tota utzato ot xcd. ry EDF. W show: If EDF fas to fd fasb schdu, th th tota utzato must xcd. Assumtos: At som tm t, Job J,c of as msss ts dad. WLOG: f mor tha o job hav dad t, bra t for J,c. 4

5 CPSC-663: Ra-m Systms Prorty-Drv Schdu Otmaty of EDF cot Cas : Currt rod of vry tas bs at or aftr r,c. Cas : Currt rod of som tas my start bfor r,c. Cas : currt rod r,c r,c Currt jobs othr tha J,c do ot xcut bfor tm t. t < U > t φ t φ t t t U J,c msss dad! Otmaty of EDF cot Cas : Som currt rods start bfor r,c. Notato: : St of a tass. : St of tass whr currt rod starts bfor r,c. - : St of tass whr currt rod start at or aftr r,c. φ' r,c r,c t : Last ot tm bfor t wh som currt job s xcutd. No currt job s xcutd mmdaty aftr tm t. Why?. A jobs ar do.. Jobs - ot yt rady. t t 5

6 CPSC-663: Ra-m Systms Prorty-Drv Schdu Cas cot t t < t t φ' t t t t U > ' ' t t φ' t t U What about assumto that rocssor vr d? fort ths art sam roof hods for ths art t Q.E.D. Statc-Prorty s ot otma! Exam: What about Statc Prorty?,, 00% 5,.5, 5 U So: Why bothr wth statc-rorty? smcty rdctabty J,3 must hav owr rorty tha J,! 6

7 CPSC-663: Ra-m Systms Prorty-Drv Schdu Urdctabty of EDF Schdu Ovr-ru jobs hod o to thr rorts Exam:,,4 3,8 Norma Orato,,4 3,8 3 ovr-rus by a bt mor tha o tm ut Urdctabty of EDF Schdu II,,4 3,8 3 ovr-rus for a bt or...,,4 3,8 h sam stuato us Rat-Mootoc Schdu: hh-rorty tass ar rotctd 7

8 CPSC-663: Ra-m Systms Prorty-Drv Schdu Schduabty Bouds for Statc-Prorty Smy-Prodc Woroads: Smy-Prodc: A st of tass s smy rodc f, for vry ar of tass, o rod s mut of othr rod. horm: A systm of smy rodc, ddt, rmtab tass whos ratv dads ar qua to thr rods s schduab accord to RM ff thr tota utzato dos ot xcd 00%. Proof: Assum msss dad at tm t. t s tr mut of. t s aso tr mut of <., Utzato du to hhst-rorty tass > tota tm to comt jobs wth dad t: If job msss dad, th U > U >. t t U t Q.E.D. Schduab Utzato of ass wth D, Us Rat-Mootoc Aorthm horm: [Lu&Layad 73] A systm of ddd, rmtab rodc tass wth D ca b fasby schdud by th RM aorthm f ts tota utzato U s ss or qua to U RM Why ot.0?, 5,,.5, 5 msss dad! Proof: Frst, show that thorm s corrct for sca cas whr ost rod < shortst rod. W rmov ths rstrcto atr. 8

9 CPSC-663: Ra-m Systms Prorty-Drv Schdu Proof of Lu&Layad Gra da: Fd th most-dffcut-to-schdu systm of tass amo a dffcut-to-schdu systms of tass. Dffcut-to-schdu: Fuy utzs rocssor for som tm trva. Ay cras xcuto tm woud ma systm uschduab. Most-dffcut-to-schdu: systm wth owst utzato amo dffcutto-schdu systms. Each of th foow 4 sts brs us cosr to ths systm. St : Idtfy hass of tass most-dffcut-to-schdu systm. Systm must b -has. ta about ths atr Proof of Lu&Layad cot St : Choos ratosh btw rods ad xcuto tms. Hyothsz that aramtrs of MDS systm ar thus ratd. Cof attto to frst rod of ach tas. ass rocssor busy ut d of rod ca ths Prorty A 9

10 CPSC-663: Ra-m Systms Prorty-Drv Schdu Proof Lu&Layad cot St 3: Show that ay st of D--S tass that ar ot ratd accord to Prorty A has hhr utzato. What has f w dvat from Prorty A? Dvat o way: Icras xcuto of som hh-rorty tas by ε: ' ε ε Must rduc xcuto tm of som othr tas: ' ε U ' U ' ' ε ε 443 > 0 Proof Lu&Layad cot Dvat othr way: Rduc xcuto tm of som hh-rorty tass by ε: ' ' ε ε Must cras xcuto tm of som owr-rorty tas: '' ε ε ε U '' U 443 > 0 0

11 CPSC-663: Ra-m Systms Prorty-Drv Schdu Proof Lu&Layad cot St 4: Exrss th tota utzato of th M-D--S tas systm whch has Prorty A. Df Fd ast ur boud o utzato: St frst drvatv of U wth rsct to ach of s to zro: : U. 0 / / j j j j j j j j U U Q.E.D. for j,,3,,- Prod Ratos > W show:. Evry D--S tas systm wth rod rato > ca b trasformd to D--S tas systm wth rod rato <.. h tota utzato of th tas st dcrass dur th trasformato st. W ca thrfor cof sarch to systms wth rod rato <.. rasformato - : Comar utzatos: d wh -,,,, wth < 0 ' > U U Q.E.D.

12 CPSC-663: Ra-m Systms Prorty-Drv Schdu Rard that Ltt Qusto about th Phas... Dfto: [Crtca Istat] [Lu&Layad] If th maxmum rsos tm of a jobs s ss tha D, th th job of rasd th crtca stat has th maxmum rsos tm. [Bar] If th rsos tm of som jobs xcds D, th th rsos tm of th job ras dur th crtca stat xcds D. horm: I a fxd-rorty systm whr vry job comts bfor th xt job th sam tas s rasd, a crtca stat of a tas occurs wh o of ts jobs J,c s rasd at th sam tm wth a job of vry hhr-rorty tas. Proof forma Assum: horm hods for <. WLOG: < : φ 0, ad w oo at J, : Obsrvato: h comto tm of hhr-rorty jobs s ddt of th ras tm of J,. hrfor: h soor J, s rasd, th or t has to wat ut t s comtd. Q.E.D.

13 CPSC-663: Ra-m Systms Prorty-Drv Schdu Proof ss forma WLOG: {,..., } 0 m φ Obsrvato: Nd oy cosdr tm rocssor s busy xcut jobs,,, - bfor φ. If rocssor d or xcuts owr-rorty jobs, or that orto of schdu ad rdf th φ s. R, φ -φ Dur trva [ φ, φ R, ] a tota of jobs bcom rady for xcuto. R, s smast souto, f such a so: R φ φ, souto xsts. R φ, ad: R, R, φ φ φ Why Utzato-Basd sts? If o aramtr vr vars, w coud us smuato. But: Excuto tms may b smar tha Itrras tms may vary. sts ar st robust. Usfu as mthodooy to df xcuto tms or rods. 3

14 CPSC-663: Ra-m Systms Prorty-Drv Schdu Otmaty of Dad-Mootoc, Rat-Mootoc horm: If a tas st ca b fasby schdud by som statc-rorty aorthm, t ca b fasby schdud by DM. Proof: Assum: A fasb schdu xsts for a tas st. h rorty assmt s,,,. For som, w hav D > D. W show that w ca swa th rorty of ad ad th rsut schdu rmas fasb. D t D m-dmad Aayss Comut tota dmad o rocssor tm of job rasd at a crtca stat ad by hhr-rorty tass as fucto of tm from th crtca stat. Chc whthr dmad ca b mt bfor dad. Dtrm whthr s schduab: Focus o a job, suos ras tm s crtca stat of : w t: Procssor-tm dmad of ths job ad a hhr-rorty jobs rasd t 0, t: hs job mts ts dad f, for som w t t t D : w t t If ths dos ot hod, job caot mt ts dad, ad systm of tass s ot schduab by v statc-rorty aorthm. 4

15 CPSC-663: Ra-m Systms Prorty-Drv Schdu Exam 3 4 3, 5, 7, 9, wt w t t Exam 3 4 3, 5, 7, 9, wt w t w t t 5

16 CPSC-663: Ra-m Systms Prorty-Drv Schdu Exam 3 4 3, 5, 7, 9, wt w 3 t w t w t t Exam 3 4 3, 5, 7, 9, wt w 4 t w 3 t w t w t t 6

17 CPSC-663: Ra-m Systms Prorty-Drv Schdu Practca Factors No-Prmtab Portos * Sf-Susso of Jobs * Cotxt Swtchs * Isuffct Prorty Rsoutos Lmtd Numbr of Dstct Prorts m-drv Immtato of Schdur c Schdu Vary Prorts Fxd-Prorty Systms Practca Factors I: No-Prmtabty Jobs, or ortos throf, may b o-rmtab. Dfto: [o-rmtab orto] ρ : arst o-rmtab orto of jobs. Dfto: [bocd job] A job s sad to b bocd f t s rvtd from xcut by owr-rorty job. rorty-vrso Wh tst schduabty of a tas, w must cosdr hhr-rorty tass ad o-rmtab ortos of owr-rorty tass 7

18 CPSC-663: Ra-m Systms Prorty-Drv Schdu Aayss wth No-Prmtab Portos Dfto: [boc tm] h boc tm b of as s th ost tm by whch ay job of ca b bocd by owr-rorty jobs: b max ρ m-dmad fucto wth boc: w t b Utzato bouds wth boc: tst o tas at a tm: t b b... U RM No-Prmtabty: Exam 3 tm-dmad fucto wth boc 3 o-rmtab 4, 5, 9, wt.5 tm-dmad fucto wthout boc t wt w 3 t w t w t t 4 6 8

19 CPSC-663: Ra-m Systms Prorty-Drv Schdu Practca Factors II: Sf-Susso Dfto: [Sf-Susso] Sf-susso of a job occurs wh th job wats for a xtra orato to comt RPC, I/O orato. Assumto: W ow th maxmum th of xtra orato;.., th durato of sf-susso s boudd. Exam: φ 0, 4,.5 sf-susso! φ 3, 7,.0 Aayss: b SS : Boc tm of du to sf-susso. SS b max. sf - susso tm of - m, max. sf - susso tm of Sf-Susso wth No-Prmtab Portos Whvr job sf-susds, t oss th rocssor. Wh trs to r-acqur rocssor, t may b bocd by tass ormtab ortos. Aayss: b NP : Boc tm du to o-rmtab ortos K : Max. umbr of sf-sussos b : ota boc tm b b SS K bnp 9

20 CPSC-663: Ra-m Systms Prorty-Drv Schdu Practca Factors III: Cotxt Swtchs Dfto: [Job-v fxd rorty assmt] I a job-v fxd rorty assmt, ach job s v a fxd rorty for ts tr xcuto. Cas I: No sf-susso I a job-v fxd-rorty systm, ach job rmts at most o othr job. Each job thrfor causs at most two cotxt swtchs hrfor: Add th cotxt swtch tm twc to th xcuto tm of job: CS Cas II: Sf-sussos ca occur Each job suffrs two mor cotxt swtchs ach tm t sf-susds hrfor: Add mor cotxt swtch tms aroraty: K CS 0