1. Real-Time Scheduling II: Compositional Scheduling Framework Insik Shin Dept. of Computer Science KAIST

2. Timing Composition  What is a problem?  How to compose two or more timing properties into a single timing property T1T1 T2T2 T3T3

3. Timing Composition  What is a problem?  How to compose two or more timing properties into a single timing property  How useful is it?  It serves as a basis for the design and analysis of component- based real-time systems  i.e., for real-time component interfaces that abstract the collective timing requirements of individual workloads within components T1T1 T2T2 T3T3

4. Hierarchical Scheduling 4 CPU Task Scheduler S Task S Application 1 (component) Application 2 (component) EDF RMEDF

5. Hierarchical Scheduling - Issues 5  System-level scheduler ’ s viewpoint CPU Task Scheduler S Task S What is the real-time requirements of each application ? Application 1Application 2

6. Hierarchical Scheduling - Issues 6 CPU  Application-level scheduler ’ s viewpoint Scheduler Task S S CPU Share Real-time guarantees from CPU supply? How can we achieve schedulability analysis with this CPU share?

7. Proposed Framework - Overview 7  Interface-based hierarchical scheduling framework CPU Scheduler Task S S interface

8. Proposed Framework - Approaches 8  Interface-based hierarchical scheduling framework  Approach  Propose a new real-time resource model (periodic)  Extend real-time scheduling theories with the new resource model  Develop interfaces with these results  Use interfaces for component-based schedulabililty analysis

9. Proposed Framework - Assumptions 9  Tasks  periodic  independent  fully preemptable  synchronously released  Uni-processor scheduling  Scheduling algorithms : EDF / RM scheduler task resource task

10. Outline 10  Compositional Real-time Scheduling Framework  Motivation   Schedulability Analysis  Component Timing Abstraction Real-Time Resource Model

11. Real-Time Resource Modeling 11  Real-time virtual resource model  Characterize the timing property of resource allocations provided to a single task (application/ component)  Previous approaches  rate-based resource model  Our approach  temporally partitioned resource model task 2task 1 scheduler resource

12. Resource Modeling  Dedicated resource  available at all times at full capacity  Rate-based shared resource  available at fractional capacity at all times  Time-shared resource  availabe at full capacity at some times time task resource task scheduler time task

13. Periodic Resource Model 13  Periodic resource model Γ ( P,Q )  a time-shared resource,  characterizes periodic resource allocations  period P and allocation time Q  Resource utilization U Γ = Q/P  Example, P = 3, Q = 2 0 1 2 3 4 5 6 7 8 9 time

14. Outline 14  Compositional Real-time Scheduling Framework  Motivation  Real-time Resource Modeling  Schedulability Analysis  Component Timing Abstraction Schedulability Analysis

15. Traditional Schedulability Analysis 15  Demand-based analysis with dedicated resource ≤ resource demand during an interval of length t Task Scheduler t

16. Schedulability Analysis 16  Demand- and supply-based analysis with periodic (time- shared) resource ≤ resource supply, during an interval of length t resource demand during an interval of length t Task Scheduler Periodic Resource

17. Resource Demand Bound  Resource demand bound function  dbf(W,A,t) : the maximum possible resource demand of a task set W under algorithm A during an interval of length t 17

18. Demand Bound Functions  For a periodic task set W = {T i (p i,e i )},  dbf (W,A,t) for EDF [Baruah et al., ‘ 90]  dbf (W,A,t,i) for RM [Lehoczky et al., ‘ 89] 18

19. Resource Supply 19  Resource supply bound function  sbf Γ (t) : the minimum resource supply by resource Γ over all intervals of length t  Periodic resource Γ (3,2) 0time Γ (3,2) t =1 t =2 t =3 t =5 t =4 t =1

20. Periodic Resource Model  Supply bound function sbf Γ (t) 20 0 1 2 3 4 5 6 7 8 9 10 t supply

21. Schedulability Condition - EDF  A periodic task set W is schedulable under EDF if and only if [Baruah et al. ’ 90] 21 over the worst-case resource supply of periodic resource model Γ (P,Q) [Shin & Lee, ’03]

22. Schedulability Condition - RM  A periodic task set W is schedulable under RM over the worst-case resource supply of periodic resource model Γ(P,Q) if and only if [Shin & Lee, ’03] 22

23. Schedulability Analysis 23  Demand- and supply-based analysis ≤ resource supply, P. Task EDF/RM Periodic Resource resource demand naturally extensible with other scheduler, task models, and/or resource models, as long as they can provide resource demand and supply bounds.

24. Outline 24  Compositional Real-time Scheduling Framework  Motivation  Resource Modeling  Schedulability Analysis  Component Timing Abstraction Component Timing Abstraction

25.  Abstracting the collective real-time requirements of a component as a single real-time requirement (real-time component interface) 25 Periodic (50,7) EDF Periodic (70,9) real-time component interface Periodic (50,7) Periodic (70,9) Real-Time Requirement EDF

26. Component Timing Abstraction  Finding a periodic resource model Γ (P,Q) that guarantees the schedulability of a component 26 Periodic (50,7) EDF Periodic (70,9) real-time component interface periodic resource Γ (P,Q) periodic interface Γ (P,Q)

27. Abstraction - Example  In this example, a solution space of a periodic resource Γ (P,Q) is 27 Γ (P,Q) Periodic (50,7) EDF Periodic (70,9)

28. Abstraction - Example  An approach to pick one out of solution space  Given a range of P, we can pick Γ (P,Q) such that U Γ is minimized. (for example, 28 ≤ P ≤ 46) 28 Γ (P,Q) Periodic (50,7) EDF Periodic (70,9) Γ (29, 9.86)

29. Abstraction 29 periodic interface Γ (29, 9.86) U W =0.27U Γ =0.34 Periodic (50,7) EDF Periodic (70,9)

30. Abstraction Overhead  Abstraction overhead (O Γ ) is 30 periodic interface Γ (29, 9.86) U W =0.27U Γ =0.34 0.34/0.27 – 1 = 0.26 Periodic (50,7) EDF Periodic (70,9)

31. Abstraction Overhead Bound  Abstraction overhead (O Γ ) is  A = EDF  A = RM 31

32. Abstraction Overhead 32  Simulation Results  with periodic tasks and periodic resource under EDF/RM  the number of tasks n : 2, 4, 8, 16, 32, 64  the workload utilization U(W) : 0.2~0.7  ratio between the resource period and minimum task period : represented by k

33. Abstraction Overhead 33  k ≈ P min /P, U W = 0.4, n = 8

34. Conclusion  Compositional scheduling framework  Allows composition of multiple timing properties into one  Provides key techniques for component-based design over real-time systems  Naturally applicable to many domains, including some systems areas such as  Hypervisor + guest OS  Distributed systems

35. Key References 35  Compositional real-time scheduling framework  Periodic, independent tasks over uniprocessor  RTSS ’03 (Best Paper), ’04, EMSOFT ’06  ACM TECS (Trans. on Embedded Computing Systems)’08  Synchronization  RTSS ’08 (Best Paper Runner-Up), EMSOFT ’07  IEEE TII (Transactions on Industrial Informatics) ’09  Multiprocessors  ECRTS ’08 (Best Paper Runner-Up)  Real-Time Systems Journal ’09