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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 - PowerPoint PPT Presentation
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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
?