Probabilistic Results for Mixed Criticality Real-Time Scheduling

Bader N. AlahmadSathish Gopalakrishnan

Example

Platform

Single ProcessorPreemptive

 

Simpler case: Independent Job Model

independent (one-shot) jobs

Job characterized by

Release Time Absolute Deadline Criticality

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

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

If an instance is WCR-schedulable on a processor it is MC-schedulable on 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.

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 – Speed up factor

The root of the equation

improvement of asymptotically over WCR

For dual-criticality systems: The Golden ration

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 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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