Overview. Eingebettete Systeme. Model of periodic tasks. Model of periodic tasks. Echtzeitverhalten und Betriebssysteme

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1 Overvew Egebettete Systeme able of some kow preemptve schedulg algorthms for perodc tasks: Echtzetverhalte ud Betrebssysteme 5. Perodsche asks statc prorty dyamc prorty Deadle equals perod Deadle smaller tha perod RM (rate-mootoc) EDF DM (deadle-mootoc) EDF* 2 Model of perodc tasks Examples: sesory data acqusto, low-level servog, cotrol loops, acto plag ad system motorg. Whe a cotrol applcato cossts of several cocurret perodc tasks wth dvdual tmg costrats, the OS has to guaratee that each perodc stace s regularly actvated at ts proper rate ad s completed wth ts deadle. Deftos: Γ : deotes a set of perodc tasks τ : deotes a geerc perodc task τ, j : deotes the jth stace of task r, j, s, j, f, j, d, j : deotes the release tme, start tme, fshg tme, absolute deadle of the jth stace of task Φ : phase of task (release tme of ts frst stace) D : relatve deadle of task Model of perodc tasks he followg hypotheses are assumed o the tasks: he staces of a perodc task are regularly actvated at a costat rate. he terval betwee two cosecutve actvatos s called perod. he release tmes satsfy All staces have the same worst case executo tme All staces of a perodc task have the same relatve deadle D. herefore, the absolute deadles satsfy, j ( j ) r, j = Φ + ( j ) D d = Φ

2 Model of perodc tasks he followg hypotheses are assumed o the tasks cot : Ofte, the relatve deadle equals the perod D = ad therefore d = Φ + j, j All perodc tasks are depedet; that s, there are o precedece relatos ad o resource costrats. No task ca susped tself, for example o I/O operatos. All tasks are released as soo as they arrve. All overheads the OS kerel are assumed to be zero. Model of perodc tasks Example τ Φ D r, r, 2 τ,3 s,3 f, Rate mootoc schedulg (RM) Assumptos: ask prortes are assged to tasks before executo ad do ot chage over tme (statc prorty assgmet). RM s trscally preemptve: the curretly executg task s preempted by a task wth hgher prorty. Deadles equal the perods D =. Algorthm: Each task s assged a prorty. asks wth hgher request rates (that s wth shorter perods) wll have hgher prortes. asks wth hgher prorty terrupt tasks wth lower prorty. Rate mootoc schedulg (RM) Optmalty: RM s optmal amog all fxed-prorty assgmets the sese that ot other fxed-prorty algorthm ca schedule a task set that caot be scheduled by RM. he proof s doe by cosderg several cases that may occur, but the ma deas are as follows: A crtcal stat for ay task occurs wheever the task s released smultaeously wth all hgher prorty tasks. he tasks schedulablty ca easly be checked at ther crtcal staces. If all tasks are feasble at ther crtcal stats, the the task set s schedulable ay other codto. Show that, gve two perodc tasks, f the schedule s feasble by a arbtrary prorty assgmet, the t s also feasble by RM. Exted the result to a set of perodc tasks. 7 8

3 Rate mootoc schedulg (RM) Schedulablty aalyss: A set of perodc tasks s schedulable wth RM f = ( 2 / ) hs codto s suffcet but ot ecessary ( geeral). he proof of ths codto s rather volved. he term U = = deotes the processor utlzato factor U whch s the fracto of processor tme spet the executo of the task set. Deadle mootoc schedulg (DM) Assumptos are as rate mootoc schedulg, but deadles may be smaller tha the perodc,.e. D Algorthm: Each task s assged a prorty. asks wth smaller deadles wll have hgher prortes. asks wth hgher prorty terrupt tasks wth lower prorty. Schedulablty aalyss: A set of perodc tasks s schedulable wth DM f ( 2 / ) = D hs codto s suffcet but ot ecessary ( geeral). 9 0 Deadle mootoc schedulg (DM) here s also a ecessary ad suffcet schedulablty test whch s computatoally more volved. It s based o the followg observatos: he worst-case processor demad occurs whe all tasks are released smultaeously; that s, at ther crtcal staces. For each task, the sum of ts processg tme ad the terferece (preempto) mposed by hgher prorty tasks must be less tha or equal to D. A measure of the worst case terferece for task ca be computed as the sum of the processg tmes of all hgher prorty tasks released before some tme t where tasks are ordered accordg to < j D < D j : t I j j= j = Deadle mootoc schedulg (DM) he logest respose tme R of a perodc task s computed, at the crtcal stat, as the sum of ts computato tme ad the terferece due to preempto by hgher prorty tasks R = + I Hece, the schedulablty test eeds to compute the smallest R that satsfes R R j j= j = + for all tasks. he, R D must hold for all tasks. It ca be show that ths codto s ecessary ad suffcet. 2

4 Deadle mootoc schedulg (DM) he logest respose tmes R of the perodc tasks ca be computed teratvely by the followg algorthm: Algorthm: DM_guaratee (Γ) { for (each τ Γ){ I = 0; do { R = I + ; f (R > D ) retur(unshedulable); I = j=,,(-) R/ j j ; } whle (I + > R); } retur(shedulable); } DM example Example: ask : = ; = 4; D = 3 ask 2: 2 = ; 2 = 5; D2 = 4 ask 3: 3 = 2; 3 = 6; D3 = 5 ask 4: 4 = ; 4 = ; D4 = 0 Algorthm for task 4: Step 0: R 4 = Step : R 4 = 5 Step 2: R 4 = 6 Step 3: R 4 = 7 Step 4: R 4 = 9 Step 5: R 4 = DM example τ U = ( 2 ) = D = > / = DM example 0 I 4 τ 2 0 τ τ

5 EDF schedulg (earlest deadle frst) Assumptos: dyamc prorty assgmet trscally preemptve D Algorthm: he curretly executg task s preempted wheever aother perodc stace wth earler deadle becomes actve. d, j = Φ + ( j ) + D Optmalty: No other algorthm ca schedule a set of perodc tasks f the set that ca ot be scheduled by EDF. he proof s smple ad follows that of the aperodc case. EDF schedulg A ecessary ad suffcet schedulablty test f D = : A set of perodc tasks s schedulable wth EDF f ad oly f he term U = = U deotes the average processor utlzato. = = 7 8 EDF schedulg If the utlzato satsfes U >, the there s o vald schedule: he total demad of computato tme terval = 2... s = U > = ad therefore, t exceeds the avalable processor tme. If the utlzato satsfes U, the there a vald schedule (proof by cotradcto): Assume that deadle s mssed at some tme t 2. EDF schedulg [ ] Wth a terval t,t 2 the total computato tme demaded by perodc tasks s bouded by t2 t t2 t p ( t, t2) = = ( t2 t )U = = Sce the deadle at tme s mssed, we must have: t umber of complete perods of task I the terval t 2 ( t t ) ( t t ) U U 2 t < p 2, 2 > 9 20

6 Perodc tasks Example: 2 tasks, deadle = perods, U = 97% 2