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Probabilistic Results for Mixed Criticality Real-Time Scheduling

Probabilistic Results for Mixed Criticality Real-Time Scheduling. Bader N. Alahmad Sathish Gopalakrishnan. Example. Platform. Single Processor Preemptive. Simpler case : Independent Job Model. independent (one-shot) jobs Job characterized by  Release Time  Absolute Deadline

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Probabilistic Results for Mixed Criticality Real-Time Scheduling

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  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 independent (one-shot) jobs Job characterized by  Release Time  Absolute Deadline  Criticality

  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 MC-Schedulability MC-Scheduling Need to find a scheduling policy…

  8. Approach: Worst Case Reservation (WCR) Scheduling

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

  10. WCR Optimal (Oracle) 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 • 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

  11. WCR-Schedulability If an instance is WCR-schedulable on a processor  it is MC-schedulableon the same processor Conversely, if an instance with criticality levels is MC-schedulable on a given processor  it is WCR-schedulable on a processor that is times as fast, and this factor is tight.

  12. 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.

  13. OCBP – Speed up factor The root of the equation  improvement of asymptotically over WCR For dual-criticality systems:  The Golden ration

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

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

  16. 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?

  17. Current InvestigationFinite 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

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