Real-Time Scheduling
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1 Real-Tme Schedulg Itroducto to Real-Tme Revew Ma vocabulary Deftos of tasks, task vocatos, release/arrval tme, absolute deadle, relatve deadle, perod, start tme, fsh tme, reemptve versus o-preemptve schedulg rorty-based schedulg Statc versus dyamc prortes tlzato () ad Schedulablty Ma problem: Fd Boud for schedulg polcy such that < Boud All deadles met! Optmalty of EDF schedulg Boud EDF 00%
2 Schedulablty Aalyss of erodc Tasks Ma problem: Gve a set of perodc tasks, ca they meet ther deadles? Depeds o schedulg polcy Soluto approaches tlzato bouds (Smplest) Exact aalyss (N-Hard) Heurstcs Two most mportat schedulg polces Earlest deadle frst (Dyamc) Rate mootoc (Statc) Schedulablty Aalyss of erodc Tasks Ma problem: Gve a set of perodc tasks, ca they meet ther deadles? Depeds o schedulg polcy Soluto approaches tlzato bouds (Smplest) Exact aalyss (N-Hard) Heurstcs Two most mportat schedulg polces Earlest deadle frst (Dyamc) Rate mootoc (Statc)
3 tlzato Bouds Itutvely: The lower the processor utlzato,, the easer t s to meet deadles. The hgher the processor utlzato,, the more dffcult t s to meet deadles. Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed Example (Rate-Mootoc Schedulg) Task Task % tme.0 3 Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 83.3%? 0 3
4 Example (Rate-Mootoc Schedulg) Task Task % tme.0 3 Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 83.3%? 0 Example (Rate-Mootoc Schedulg) Task Mssed deadle! Task tme.0 3 schedulable Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 83.3% 00% 83.3%? 0 4
5 Aother Example (Rate-Mootoc Schedulg) Task Task tme.4 6 Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 90% 00% 83.3%? 0 Aother Example (Rate-Mootoc Schedulg) Task Task tme.4 6 Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 90% 00% 83.3%? 0 5
6 Aother Example (Rate-Mootoc Schedulg) Task Task tme.4 6 Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 90% Schedulable! 00% 90% 83.3%? 0 Aother Example (Rate-Mootoc Schedulg) Task Task tme.4 6 Schedulablty depeds o task set! No clea utlzato threshold betwee schedulable ad uschedulable task sets! Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed 90% Schedulable! 00% 90% 83.3%? 0 6
7 A oceptual Vew of Schedulablty tlzato Schedulable schedulable Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles are mssed Task Set A oceptual Vew of Schedulablty tlzato Schedulable schedulable All gree area (schedulable)? Modfed Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles may or may ot be mssed Task Set 7
8 A oceptual Vew of Schedulablty tlzato Schedulable schedulable < boud s a suffcet but ot ecessary schedulablty codto All gree area (schedulable)? Modfed Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles may or may ot be mssed Task Set A oceptual Vew of Schedulablty tlzato Equvalet questo: What s the lowest utlzato of a uschedulable task set? Schedulable schedulable All gree area (schedulable)? Modfed Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles may or may ot be mssed Task Set 8
9 A oceptual Vew of Schedulablty tlzato Equvalet questo: What s the lowest utlzato of a uschedulable task set? (alled the tlzato Boud, boud ) Schedulable schedulable crtcally All gree area (schedulable)? Modfed Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles may or may ot be mssed Task Set Soluto Approach: Look at rtcally-schedulable Task Sets tlzato tlzato decreases wth x ase (a) Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) ase (b) tlzato creases wth x All gree area (schedulable)? Modfed Questo: s there a threshold boud such that Whe < boud deadles are met Whe > boud deadles may or may ot be mssed Task Set 9
10 Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) 0
11 Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Task Task rtcally Fd some task set parameter x schedulable such that ase (a): x<x total o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o )
12 Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Task Task? Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder a smple case: tasks Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o )
13 Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): > Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) 3
14 Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): > Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): > Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) 4
15 Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): > Task Task Fd some task set parameter x such that ase (a): x<x o (x) decreases wth x ase (b): x>x o (x) creases wth x Thus (x) s mmum whe xx o Fd (x o ) Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): ase (b): > Task Task ( ) 5
16 6 Dervg the tlzato Boud for Rate Mootoc Schedulg osder these two sub-cases: ase (a): Task Task ase (b): > ) ( Dervg the tlzato Boud for Rate Mootoc Schedulg The mmum utlzato case: Task Task
17 7 Dervg the tlzato Boud for Rate Mootoc Schedulg The mmum utlzato case: Task Task 0 d d 0.83 Note that Geeralzg to N Tasks
18 8 Geeralzg to N Tasks d d 0 3 d d d d Geeralzg to N Tasks d d 0 3 d d d d
19 Geeralzg to N Tasks d 0 d d 0 d d 0 d 4 3 l erodc Tasks erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty 9
20 erodc Tasks erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty omg p erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty 0
21 Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles, so ca RM.
22 Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles, so ca RM Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles, so ca RM
23 Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles, so ca RM Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles, so ca RM 3
24 Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles the worst case scearo, so ca RM. How to prove t? Rate Mootoc otued Rate mootoc schedulg s the optmal fxed-prorty schedulg polcy for perodc tasks. Optmalty (Tral #): If ay other fxed-prorty schedulg polcy ca meet deadles the worst case scearo, so ca RM. How to prove t? osder the worst case scearo If someoe else ca schedule the RM ca 4
25 The Worst-ase Scearo Q: Whe does a perodc task, T, experece the maxmum delay? A: Whe t arrves together wth all the hgher-prorty tasks (crtcal stace) Idea of roof If some hgher-prorty task does ot arrve together wth T, algg the arrval tmes ca oly crease the completo tme of T roof (ase ) Task Task ase : hgher prorty task s rug whe task arrves 5
26 roof Task Task ase : hgher prorty task s rug whe task arrves shftg task rght wll crease completo tme of roof Task Task Task ase : hgher prorty task s rug whe task arrves shftg task rght wll crease completo tme of Task 6
27 roof (ase ) Task Task ase : processor s dle whe task arrves roof (ase ) Task Task ase : processor s dle whe task arrves shftg task left caot decrease completo tme of 7
28 roof (ase ) Task Task Task ase : processor s dle whe task arrves shftg task left caot decrease completo tme of Task Optmalty of Rate Mootoc If ay other polcy ca meet deadles so ca RM olcy X meets deadles? 8
29 Optmalty of Rate Mootoc If ay other polcy ca meet deadles so ca RM YES olcy X meets deadles? RM meets deadles omg p erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty 9
30 omg p erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty tlzato Boud of EDF Why s t 00%? osder a task set where: Image a polcy that reserves for each task a fracto f of each clock tck, where f / lock tck 30
31 tlzato Boud of EDF Image a polcy that reserves for each task a fracto f of each tme ut, where f / lock tck Ths polcy meets all deadles, because wth each perod t reserves for task a total tme Tme f ( / ) (.e., eough to fsh) tlzato Boud of EDF ck ay two executo chuks that are ot EDF order ad swap them 3
32 tlzato Boud of EDF ck ay two executo chuks that are ot EDF order ad swap them Stll meets deadles! tlzato Boud of EDF ck ay two executo chuks that are ot EDF order ad swap them Stll meets deadles! Repeat swap utl all EDF order EDF meets deadles 3
33 erodc Tasks erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty Doe erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty 33
34 34 Exercse: Kow Your Worst ase Scearo osder a perodc system of two tasks Let / (for,) What s the maxmum value of: Π ( ) for a schedulable system? Dervg the tlzato Boud for Rate Mootoc Schedulg The mmum utlzato case: Task Task ( )
35 35 Dervg the tlzato Boud for Rate Mootoc Schedulg The mmum utlzato case: Task Task Task Task Dervg the tlzato Boud for Rate Mootoc Schedulg The mmum utlzato case: Task Task Task Task
36 36 Solutos ( ) rtcally Schedulable Schedulable ( ) Solutos ( ) rtcally Schedulable Schedulable ( )
37 37 Solutos ( ) rtcally Schedulable Schedulable ( ) Solutos ( ) rtcally Schedulable Schedulable ( )
38 38 The Geeral ase ( )... 3 rtcally Schedulable Schedulable ( ) The Geeral ase ( )... 3 rtcally Schedulable Schedulable ( )
39 39 The Geeral ase ( )... 3 rtcally Schedulable Schedulable ( ) The Geeral ase ( )... 3 rtcally Schedulable Schedulable ( )
40 The Hyperbolc Boud for Rate Mootoc Schedulg A set of perodc tasks s schedulable f: ( ) The Hyperbolc Boud for Rate Mootoc Schedulg A set of perodc tasks s schedulable f: It s a better boud tha Example: ( ) ( / ) A system of two tasks wth 0.8, 0. 40
41 The Hyperbolc Boud for Rate Mootoc Schedulg A set of perodc tasks s schedulable f: It s a better boud! Example: ( ) A system of two tasks wth 0.8, 0. Lu ad Laylad boud: 0.9 > 0.83 The Hyperbolc Boud for Rate Mootoc Schedulg A set of perodc tasks s schedulable f: It s a better boud! Example: ( ) A system of two tasks wth 0.8, 0. Lu ad Laylad boud: 0.9 > 0.83 Hyperbolc boud ( )( ).8 x..98 < 4
42 Schedulg Taxoomy erodc Task Schedulg Rate Mootoc EDF Boud Optmalty Boud Optmalty Schedulg Taxoomy erodc Task Schedulg Rate Mootoc EDF Hyperbolc Boud Boud Optmalty Boud Optmalty 4
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