1. Towards optimal priority assignments for real-time tasks with probabilistic arrivals and probabilistic execution times Dorin MAXIM INRIA Nancy Grand Est RTSOPS, PISA, ITALY 10/07/2012

2. RTSOPS, PISA, ITALY 10/07/2012 2/7 Model of the Probabilistic Real-Time System n independent tasks with independent jobs a task τ i is characterized by τ i = ( T i, C i, D i ), period probabilistic execution time deadline (constrained) single processor, synchronous, preemptive, fixed priorities The goal: Assigning priorities to tasks so that each task meets certain conditions referring to its timing failures.

3. Probabilistic Period Probabilistic ET MIT WCET RTSOPS, PISA, ITALY 10/07/2012 3/7

4. Example RTSOPS, PISA, ITALY 10/07/2012 4/7

5. Example RTSOPS, PISA, ITALY 10/07/2012 4/7

6. Example RTSOPS, PISA, ITALY 10/07/2012 4/7

7. Example 0 1 2 3 4 T 1,0 = 1 RTSOPS, PISA, ITALY 10/07/2012 4/7

8. Example 0 1 2 3 4 T 1,0 = 1 T 2,0 = 2 RTSOPS, PISA, ITALY 10/07/2012 4/7

9. Example 0 1 2 3 4 T 1,0 = 1 T 2,0 = 2 RTSOPS, PISA, ITALY 10/07/2012 4/7

10. Example Probability of occurrence = 0.42 0 1 2 3 4 T 1,0 = 1 T 2,0 = 2 RTSOPS, PISA, ITALY 10/07/2012 4/7

11. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

12. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

13. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

14. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

15. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

16. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

17. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

18. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

19. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7

20. Example 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 T 2,0 = 4 RTSOPS, PISA, ITALY 10/07/2012 4/7 Probability of occurrence = 3.24 * 10 -6

21. Open problems RTSOPS, PISA, ITALY 10/07/2012 5/7

22. Open problems 1.Algorithm for computing the response time distribution of different jobs of the given tasks. RTSOPS, PISA, ITALY 10/07/2012 5/7

23. Open problems 1.Algorithm for computing the response time distribution of different jobs of the given tasks. 2.Priority assignment so that each task meets certain conditions referring to its timing failures. RTSOPS, PISA, ITALY 10/07/2012 5/7

24. Open problems 1.Algorithm for computing the response time distribution of different jobs of the given tasks. 2.Priority assignment so that each task meets certain conditions referring to its timing failures. 3.Study interval. RTSOPS, PISA, ITALY 10/07/2012 5/7

25. Intuitions and counter-intuitions Rate Monotonic is NOT optimal for probabilistic systems: RTSOPS, PISA, ITALY 10/07/2012 6/7

26. Intuitions and counter-intuitions Rate Monotonic is NOT optimal for probabilistic systems: RM does not take into account the probabilistic character of the tasks RTSOPS, PISA, ITALY 10/07/2012 6/7

27. Intuitions and counter-intuitions Rate Monotonic is NOT optimal for probabilistic systems: RM does not take into account the probabilistic character of the tasks RM considers tasks periods, which here are random variables that may not be comparable RTSOPS, PISA, ITALY 10/07/2012 6/7

28. Intuitions and counter-intuitions Rate Monotonic is NOT optimal for probabilistic systems: RM does not take into account the probabilistic character of the tasks RM considers tasks periods, which here are random variables that may not be comparable RM was proved not optimal for tasks with deterministic arrivals and probabilistic executions times RTSOPS, PISA, ITALY 10/07/2012 6/7

29. Thank you! RTSOPS, PISA, ITALY 10/07/2012 7/7