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

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Presentation transcript:

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

Example

Platform Single Processor Preemptive

Simpler case : Independent Job Model

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

Execution behaviours

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

Complexity results

Approach: Worst Case Reservation (WCR) Scheduling

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

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

WCR-Schedulability

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.

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

OCBP – Speed up factor

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

Probabilistic execution times to guide execution time allocation Mutually independent

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?

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

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

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

Policy – High Level Description

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

?