Timed Automata with Asynchronous Processes: Schedulability and Decidability

In this paper, we exend timed automata with asynchronous processes i.e. tasks triggered by events as a model for real-time systems. The model is expressive enough to describe concurrency and synchronization, and real time tasks which may be periodic, sporadic, preemptive and (or) non-preemptive. We generalize the classic notion of schedulability in scheduling theory to timed automata as follows. An automaton is schedulable if there exists a (preemptive or non-preemptive) scheduling strategy such that all possible sequences of events accepted by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our main result is that the schedulability checking problem is decidable To our knowledge, this is the first general decidability result on automata-theoretic models for real time scheduling without assuming that preemptions occur only at integer time points. The proof is based on a class of updatable automata: timed automata with subtraction in which clocks may be updated by subtractions. We show that if each clock is bounded with a maximal constant and subtraction operations are performed on clocks only in the bounded zone, the reachability problem is decidable. The crucial observation is that the schedulability checking problem can be encoded as a reachability problem for such automata using clock subtractions. Based on the proof, we have developed a symbolic technique, which has been implemented as a prototype tool for schedulability analysis.