From Instantaneous Schedulability to Worst Case Schedulability: A Significant Moment Approach

TL;DR

This paper unifies instantaneous and worst-case schedulability analyses for preemptive periodic systems using a significant moment approach, providing a rigorous foundation for identifying critical worst-case instants.

Contribution

It derives classical worst-case schedulability conditions from instantaneous analysis, unifying the two notions and clarifying the nature of critical worst-case moments.

Findings

Critical time instants are the worst case for scheduling.

Worst-case moments are not limited to critical instants.

Provides a rigorous justification for worst-case analysis methods.

Abstract

The method of significant moment analysis has been employed to derive instantaneous schedulability tests for real-time systems. However, the instantaneous schedulability can only be checked within a finite time window. On the other hand, worst-case schedulability guarantees schedulability of systems for infinite time. This paper derives the classical worst-case schedulability conditions for preemptive periodic systems starting from instantaneous schedulability, hence unifying the two notions of schedulability. The results provide a rigorous justification on the critical time instants being the worst case for scheduling of preemptive periodic systems. The paper also show that the critical time instant is not the only worst case moments.