From instantaneous schedulability to worst case schedulability: a significant moment approach

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