1. Probabilistic Results for Mixed Criticality Real-Time Scheduling Bader N. Alahmad Sathish Gopalakrishnan

2. Example

3. Platform Single Processor Preemptive

4. Simpler case : Independent Job Model

5. Job Criticality Codifies (potential) overload conditions In overload, jobs with higher criticality have infinite marginal utility of execution over lower criticality ones

6. Execution behaviours

7. MC-Schedulability/Scheduling Need to find a scheduling policy… MC-Schedulability MC-Scheduling

8. Complexity results

9. Approach: Worst Case Reservation (WCR) Scheduling

10. Performance Metric? How to quantify the quality of the solution ? Resource Augmentation  Processor speed up factor 1 Processor is a unit capacity bin

11. WCR Optimal (Oracle) If system criticality level = 1 : all criticality 1 jobs execute and are allowed to fully utilize the processor If system criticality level = 2 : all criticality 2 jobs execute and are allowed to fully utilize the processor WCR If system criticality level = 1 : all criticality 1 jobs execute and are allowed to fully utilize the processor If system criticality level = 2 : all jobs execute and are allowed to fully utilize the processor

12. WCR-Schedulability

13. Own Criticality Based Priority ( OCBP ) Construct fixed priority table offline. At each scheduling decision point, dispatch the job with the highest priority. Priorities assigned using Audsley’s/Lawler’s method.

14. OCBP – Priority table construction Sanjoy Baruah, Scheduling Issues in Mixed-Criticality Systems

15. OCBP – Speed up factor

16. Deterministic results are based on adversarial/worst-case behaviour.

17. Probabilistic execution times to guide execution time allocation Mutually independent

18. Open Questions What is a policy that minimizes expected lateness? – Based on expected criticality level. – Lateness: Response Time – Deadline. What is a policy that minimizes tardiness/lateness ratio? – Tardiness ratio: Response Time/Deadline. What is a policy that minimizes the probability of a deadline miss?

19. Current Investigation Finite Horizon Bandit Process Dynamic Allocation Indexes (DAI)  e.g., Gittins Index for multi-armed bandit processes Model as Markov Decision Processes Class of Optimal Stopping Problems Dropping times and time(s) to engage in job execution are random

20. If execution-time allocated to jobs so far is a random variable 

21. When and how many times to pull every bandit arm such that our expected overall reward is maximized ? Every slot machine is available for a limited time  deadlines Reward  processing time allocated Punishment  money we pay to play (how much closer we got to the deadline by the reward allocation) Weighted by job criticality n jobs

22. Policy – High Level Description

23. Prover (Scheduling Algorithm) Randomized/deterministic Adversary (randomized) Polynomial (in n ) number of communication rounds

24. ?