1. 26 April 20041 A Compositional Framework for Real-Time Guarantees Insik Shin and Insup Lee Real-time Systems Group Systems Design Research Lab Dept. of Computer and Information Science University of Pennsylvania

2. SDRL & RTG Depart. Of Computer and Information Science 26 April 20042 Scheduling Framework Example CPU OS Scheduler Digital ControllerMultimediaPeriodic Task T(p,e) T 1 (25, 5) Periodic Task T(p,e) T 2 (33, 10)

3. SDRL & RTG Depart. Of Computer and Information Science 26 April 20043 Motivating Example CPU OS Scheduler Java Virtual Machine J 1 (25,4)J 2 (40,5) VM Scheduler Multimedia T 2 (33,10) Digital Controller T 1 (25,5)

4. SDRL & RTG Depart. Of Computer and Information Science 26 April 20044 VM Scheduler’s Viewpoint CPU OS Scheduler Multimedia T 2 (33,10) Digital Controller T 1 (25,5) Java Virtual Machine J 1 (25,4)J 2 (40,5) VM Scheduler CPU Share Real-Time Guarantee on CPU Supply

5. SDRL & RTG Depart. Of Computer and Information Science 26 April 20045 Problems & Approach I Resource supply modeling –Characterize temporal property of resource allocations we propose a periodic resource model –Analyze schedulability with the new resource model Java Virtual Machine J 1 (25,4)J 2 (40,5) VM Scheduler Periodic CPU Share

6. SDRL & RTG Depart. Of Computer and Information Science 26 April 20046 OS Scheduler’s Viewpoint CPU OS Scheduler Java Virtual Machine J 1 (25,4)J 2 (40,5) VM Scheduler Multimedia T 2 (33,10) Digital Controller T 1 (25,5) Real-Time TaskReal-Time Demand

7. SDRL & RTG Depart. Of Computer and Information Science 26 April 20047 Problem II Real-Time Composition –Combine multiple real-time requirements into a single real-time requirement guaranteeing schedulability –Example: periodic task model T(p,e) Real-Time Constraint Real-Time Constraint Real-Time Constraint EDF/RM T 1 (3, 1)T 2 (4, 1)T (?, ?)

8. SDRL & RTG Depart. Of Computer and Information Science 26 April 20048 Approach I I Simple approach : T(p,e) –p = LCM (T 1, T 2 ) LCM (T 1, T 2 ) = T 1 xN 1 = T 2 xN 2 –e = p x (U 1 + U 2 ), U i = e i /p i EDF T 1 (3, 1)T 2 (4, 1)T (12, 7) T (?, ?) (12,7)T 510151203 Deadline Miss !

9. SDRL & RTG Depart. Of Computer and Information Science 26 April 20049 Approach II Our approach : periodic task model T(p,e) EDF T 1 (3, 1)T 2 (4, 1)T (2, 4/3) (12,7)T 510151203 (12,7)T 10151203246 8

10. SDRL & RTG Depart. Of Computer and Information Science 26 April 200410 Outline 1.Scheduling component modeling Periodic resource model 2.Scheduling component schedulability analysis 3.Scheduling component composition Combine the real-time guarantees of multiple components into the real-time guarantee of a single component

11. SDRL & RTG Depart. Of Computer and Information Science 26 April 200411 Scheduling Component Modeling Scheduling –assigns resources to workloads by algorithms Scheduling Component Model : M(W,R,A) –W : workload model –R : resource model –A : scheduling algorithm Resource Scheduler WorkloadPeriodic TaskWorkloadPeriodic Task EDF / RM ???

12. SDRL & RTG Depart. Of Computer and Information Science 26 April 200412 Resource Modeling Dedicated resource –Available all the time at its full capacity 0time

13. SDRL & RTG Depart. Of Computer and Information Science 26 April 200413 Resource Modeling Dedicated resource –Available all the time at its full capacity Fractional resource (slow resource) –Available all the time at its fractional capacity 0time

14. SDRL & RTG Depart. Of Computer and Information Science 26 April 200414 Resource Modeling Dedicated resource –Available all the time at its full capacity Fractional resource (slow resource) –Available all the time at its fractional capacity Partitioned resource [FeMo ’02] –Available all some times at its full capacity 0time

15. SDRL & RTG Depart. Of Computer and Information Science 26 April 200415 Resource Modeling Dedicated resource –Available all the time at its full capacity Fractional resource (slow resource) –Available all the time at its fractional capacity Partitioned resource –Available all some times at its full capacity Periodic resource R(period, allocation time) (ex. R(3,2)) –Available periodically at its full capacity 0time

16. SDRL & RTG Depart. Of Computer and Information Science 26 April 200416 T 2 (20,4)T 1 (10,2) Scheduling Component Analysis Schedulability conditions –Exact conditions for EDF/RM Schedulability bounds –Utilization bounds for periodic workload under EDF/RM –Capacity bounds for periodic resource under EDF/RM Periodic Resource Scheduler Periodic Task EDF / RM

17. SDRL & RTG Depart. Of Computer and Information Science 26 April 200417 Schedulability Conditions (EDF) Scheduling component M(W,R,EDF) is schedulable iff for all interval length t, demand w (EDF,t) ≤ supply R (t) [RTSS03] –demand w (EDF,t) : the maximum resource demand of workload W for an interval length t –supply R (t) : the minimum resource supply by resource R for an interval length t demand(EDF,t) =

18. SDRL & RTG Depart. Of Computer and Information Science 26 April 200418 supply = supply R (3) = 1 0time 0 3 1 R(3,2) t

19. SDRL & RTG Depart. Of Computer and Information Science 26 April 200419 Schedulability Conditions (RM) Scheduling component M(W,R,RM) is schedulable iff for all task T i (p i,e i ), r i (R) ≤ p i [RTSS03] –r i (R): the maximum response time of task T i over R. the smallest time t s.t. demand(RM,i,t) ≤ supply R (t) demand(RM,i,t) =

20. SDRL & RTG Depart. Of Computer and Information Science 26 April 200420 Schedulability Conditions (RM) Scheduling component M(W,R,RM) is schedulable iff for all task T i (p i,e i ), r i (R) ≤ p i [RTSS03] –Example of finding the maximum response time r i (R) time resource demand r i (R) demand(RM,i,t) supply R (t)

21. SDRL & RTG Depart. Of Computer and Information Science 26 April 200421 Motivating Example for Capacity Bound Given a task group G such that –Scheduling algorithm : EDF –A set of periodic tasks : { T 1 (3,1), T 2 (7,1) }, model the timing requirements of the task group with a periodic task model G (3, 1.43) based on utilization does not work !! 1043265987 Deadline miss for T 2

22. SDRL & RTG Depart. Of Computer and Information Science 26 April 200422 Motivating Example (2) Given a task group G such that –Scheduling algorithm : EDF –A set of periodic tasks : { T 1 (3,1), T 2 (7,1) }, model the timing requirements of the task group with a periodic task model G (3, 2.01) works !! 1043265987

23. SDRL & RTG Depart. Of Computer and Information Science 26 April 200423 Capacity Bounds Resource capacity –For a periodic resource R(p,e), its capacity is e/p. Capacity bound of a component C(W, R(p,e), A) : CB(C) –C is schedulable if CB(C) ≤ e/p How to get the capacity bounds of C(W,R(p,e),A) –assumption: the period p of R is given. –using the exact schedulability conditions, we can get the minimum capacity of R satisfying the condition. T 1 (25,4) T 2 (40,5) EDF R(10, ? ) R(10, 3.1) CB(C) = 3.1/10

24. SDRL & RTG Depart. Of Computer and Information Science 26 April 200424 Compositional Real-Time Guarantees T 11 (25,4) T 12 (40,5) T 21 (25,4) T 22 (40,5) R(?, ?) EDF RM R 2 (?, ?)R 1 (?, ?)R 1 (10, 3.1)R 2 (10, 4.34)

25. SDRL & RTG Depart. Of Computer and Information Science 26 April 200425 Compositional Real-Time Guarantees T 21 (25,4) T 22 (40,5) R(?, ?) EDF RM R(5, 4.4) R 2 (10, 4.4) T 2 (10, 4.4) T 11 (25,4) T 12 (40,5) EDF R 1 (10, 3.1) T 1 (10, 3.1)

26. 26 April 200426 Conclusion Summary –Periodic resource model –Scheduling component modeling and anaylsis –Scheduling component composition Future work –To evaluate the composition overhead in current framework –To extend our framework with other resource models for Efficient composition w.r.t utilization and complexity Ensure composition properties, i.e., –C 1 || (C 2 || C 3 ) = (C 1 || C 2 ) || C 3 –|| (C 1, C 2, C 3 ) = || (||(C 1, C 2 ), C 3 )

27. SDRL & RTG Depart. Of Computer and Information Science 26 April 200427 THE THE END END THE THANK YOU

28. SDRL & RTG Depart. Of Computer and Information Science 26 April 200428 Schedulability Conditions (EDF) Scheduling component M(W,R,EDF) is schedulable iff for all interval length t, demand w (t) ≤ t [BHR90] demand w (t) ≤ supply R (t) –demand w (t) : the maximum resource demand of workload W over all intervals of length t –supply R (t) : the minimum resource supply by resource R over all intervals of length t Resource demand in an interval Resource supply during the interval (from a dedicated resource)

29. SDRL & RTG Depart. Of Computer and Information Science 26 April 200429 Scheduling component M(W,R,RM) is schedulable iff for all task T i (p i,e i ), r i ≤ p i [AB+93] duration R (r i ) ≤ p i –r i : the maximum response time of task T i : the maximum resource demand of W to finish T i –duration R (t) : the maximum time that resource R takes to supply a t-time-unit resource Schedulability Conditions (RM) Duration to receive r i -time-unit resource allocation Deadline to receive r i -time-unit resource allocation Max. Duration to receive r i -time-unit resource allocation Deadline to receive r i -time-unit resource allocation