We study schedulability problems of timed systems with non-uniformly
recurring computation tasks. Assume a set of real time tasks whose best
and worst execution times, and deadlines are known. We use timed automata
to describe the arrival patterns (and release times) of tasks. From the
literature, it is known that the schedulability problem for a large class
of such systems is decidable and can be checked efficiently.
In this paper, we provide a summary on what is decidable and what is
undecidable in schedulability analysis using timed automata. Our main
technical contribution is that the schedulability problem will be
undecidable if these three conditions hold: (1) the execution times of
tasks are intervals, (2) a task can announce its completion time, and (3)
a task can preempt another task. We show that if one of the above three
conditions is dropped, the problem will be decidable. Thus our result can
be used as an indication in identifying classes of timed systems that can
be analysed efficiently.