Example: scheduling using EDF

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1 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Real-Time Sysems Specificaion Implemenaion Dynamic scheduling -- Earlies-deadline-firs scheduling Processor-demand analysis Verificaion Example: scheduling using EDF Problem: Assume a sysem wih asks according o he figure below. The iming properies of he asks are given in he able. Invesigae he schedulabiliy of he asks when EDF is used. (Noe ha D i < T i for all asks) Task C i D i T i 4 8

2 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Example: scheduling using EDF Simulae an execuion of he asks: misses is deadline! The asks are no schedulable even hough U = = 7 8 = < Feasibiliy analysis for EDF Wha analysis mehods are suiable for general EDF: Uilizaion-based analysis? No suiable! No general enough or exac enough Does no work well for he case of D i < T i Response-ime analysis? No suiable! Analysis much more complex han for DM Criical insan does no necessarily occur when all asks arrive a he same ime for he firs ime. Insead, response ime of a ask is maximized a some scenario where all oher asks arrive a he same ime; he wors such scenario has o be idenified for each ask before he response ime of ha ask can be calculaed.

3 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Processor-demand analysis Processor demand: The processor demand for a ask in a given ime inerval [ 0, ] is he amoun of processor ime ha he ask needs in he inerval in order o mee he deadlines ha fall wihin he inerval. e N represen he number of insances of ha mus i i complee execuion before. The oal processor demand up o is i C P (0, ) = n i= N i C i Processor-demand analysis Processor demand: N i We can calculae by couning how many imes ask has arrived during he inerval 0, D i. We can ignore insances of he ask ha arrived during he inerval D i, since D i > for hese insances. Insance wih D i > i N = N = 0

4 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Processor-demand analysis Processor-demand analysis: We can express N i as N i = D i T i + The oal processor demand is hus C P (0, ) = n i= D i T i + C i Exac feasibiliy es for EDF (Sufficien and necessary condiion) A sufficien and necessary condiion for earliesdeadline-firs scheduling, for which D i T i, is : C P (0, ) where C P (0, ) is he oal processor demand in [ 0, ]. The processor-demand analysis and associaed feasibiliy es was presened by S. Baruah,. Rosier and R. Howell in

5 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Exac feasibiliy es for EDF (Sufficien and necessary condiion) How large inerval mus be examined? arges inerval is CM of he ask s periods This inerval can be furher shorened (see course book) How many ime poins mus be examined? Only absolue deadlines need o be examined The se of deadlines can be furher reduced (see course book) The es can consequenly be improved as follows: K = K : C P (0, ) { D ik D ik = kt i + D i, D ik CM{ T,,T n }, i n, k 0} Example: scheduling using EDF Problem: Assume a sysem wih asks according o he figure below. The iming properies of he asks are given in he able. a) Deermine, by analyzing he processor demand, wheher he asks are schedulable or no using EDF. b) Deermine, by using simulaion, wheher he asks are schedulable or no using EDF. Task C i D i T i We solve his on he blackboard! 5

6 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Exended processor-demand analysis The es can be exended o handle: Blocking Sar-ime variaions ( release jier ) Time offses In his course, we only sudy blocking. Deadline inversion normal execuion criical region H blocked H and share resource R H misses is deadline H M 6

7 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Sack Resource Policy (SRP) The asks are assigned preempion levels, he properies of which are: The preempion level of ask i is denoed π i Task i is no allowed o preemp anoher ask j unless π i > π j If i has higher prioriy han j and arrives laer, hen i mus have a higher preempion level han. Noe: - The preempion levels are saic values, even hough he asks prioriies may be dynamic. - For EDF scheduling, suiable levels can be derived if asks wih shorer relaive deadlines ge higher preempion levels, ha is: π i > π j D i < D j j Sack Resource Policy (SRP) Deadline inversion can be reduced wih resource ceilings:. Each shared resource is assigned a ceiling ha is always equal o he maximum preempion level among all asks ha may be blocked when requesing he resource.. The proocol keeps a sysem-wide ceiling ha is equal o he maximum of he curren ceilings of all resources.. A ask wih he earlies deadline is allowed o preemp only if is preempion level is higher han he sysem-wide ceiling. Noe: The original prioriy of he ask is no changed a run-ime. The resource ceiling is a dynamic value calculaed a run-ime as a funcion of curren resource availabiliy. Oherwise, he behavior of he SRP proocol is very similar o he ICPP, and SRP also exhibis idenical properies regarding maximum blocking ime and freedom from deadlock. 7

8 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Sack Resource Policy (SRP) normal execuion preempion level (H) > preempion level (M) > preempion level () H and share resource R criical region sysem-wide ceiling is se o R s resource ceiling (= H s preempion level) H blocked sysem-wide ceiling is resored H M Again: noe he similariy o he behavior of ICPP Exended processor-demand analysis Blocking can be accouned for in he following way: B i Blocking facor represens he lengh of criical / nonpreempive regions ha are execued by asks wih lower preempion levels han i Tasks are indexed in he order of increasing preempion levels, ha is: π i > π j i < j K, i [, n ]: C Pi (0, ) i i D C P = k T k + C k + k = D i T i + B i 8

9 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Exended processor-demand analysis Deermining he blocking facor for ask i :. Deermine he wors-case resource ceiling for each criical region, ha is, assume he run-ime siuaion where he corresponding resource is unavailable.. Idenify he asks ha have a preempion level lower han and ha calls criical regions wih a wors-case resource ceiling equal o or higher han he preempion level of i.. Consider he imes ha hese asks lock he acual criical regions. The longes of hose imes consiues he blocking facor. B i i Example: scheduling using EDF Problem: Assume a sysem wih asks according o he figure below. The iming properies of he asks are given in he able. Three resources R, R and R have hree, one, and hree unis available, respecively. The parameers H R, H R and H R represen he longes ime a ask may use he corresponding resource. The parameers μ R, μ R and μ R represen he number of unis a ask requess from he corresponding resource. R R Task Task Ci i Di D i Ti i R H R H R - H R μ R μ R μ R - 9

10 EDA/DIT6 Real-Time Sysems, Chalmers/GU, 0/0 ecure #4 Updaed February, 0 Example: scheduling using EDF Problem: (con d) Task firs requess R and hen, while using R, requess R Task firs requess R and hen, while using R, requess R; hen, afer releasing he wo resources, requess R Task firs requess R and hen, while using R, requess R; hen, afer releasing he wo resources, requess R Examine he schedulabiliy of he asks when he SRP (Sack Resource Policy) proocol is used. a) Derive he ceilings (dynamic and wors-case) of he resources. b) Derive he blocking facors for he asks. c) Show wheher he asks are schedulable or no. We solve his on he blackboard! Feasibiliy ess Summary D i = T i D i T i Saic prioriy (RM/DM) U n( / n ) i : R i = C i + j hp(i) R i T j C j D i Dynamic prioriy (EDF) U : n i= D i T i + C i 0

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T