Algebraic Techniques for Timed Systems

1 M o t i v a t i o n s Performance evaluation is a central issue in the design of complex real-time systems. The general situation we consider in this paper can be described as follows : 1 / T h e real-time system in consideration consists of a finite collection of tasks. Tasks are triggered by events originating from both the environment and the system itself, depending on its internal state. 2/ Tasks can be concurrent or serialized, depending on their causality interactions. And this may change dynamically depending on the s tate of the environment and of the system itself. 3/ Tasks need resources for their completion, and they wait until all resources needed axe available. Restrictions axe listed next : 1 / B o t h system and environment states can take a f in i te number of values. If this is not the case, then some kind of abstract ion is needed to enforce this situation (e.g., values of integer s tate variables are abstracted). 2/ State transitions are not triggered by the await ing/reception of resources, i.e., watchdog/ t imeout mechanisms axe not modelled. Again, if * This work is supported in part by Esprit LTR-SYRF project (EP 22703).