We present anoverview and synthesis of existing results about process algebras for the speci cation and analysis of timed systems. The motivation is double: present anoverview of some relevant and representative approaches and suggest a unifying framework for them. time, we propose a general model for them: transition systems whose labels are either elements ofavocabulary of actions or elements of a time domain. Many properties of this model are studied concerning their impact on description capabilities and on realisability issues. An overview of the language features of the process algebras considered is presented, by focusing on constructs used to express time constraints. The presentation is organised as an exercise of building a timed process algebra from a standard process algebra for untimed systems. The overview is completed by a discussion about description capabilities according to semantic and pragmatic criteria. 1

We study a process algebra ATP for the description and analysis of systems of timed processes. An important feature of the algebra is that its vocabulary of actions contains a distinguished element . An occurrence of is a time event representing progress of time. The algebra has, apart from standard operators of process algebras like CCS or ACP, a primitive binary unit-delay operator. For two arguments, processes P and Q, this operator gives a process which behaves as P if started before the occurrence of a time action and as Q otherwise. From this operator we define d-unit delay operators that can model delay constructs of languages, like timeouts or watchdogs. The use of such operators is illustrated by examples. ATP is provided with a complete axiomatisation with respect to strong bisimulation semantics. It is shown that the algebras obtained by adding the various d-unit delay operators to ATP are conservative extensions of it.

The paper presents results of ongoing work aiming at the unification of some behavioral description formalisms for timed systems. We propose for the algebra of timed processes ATP a very general semantics in terms of a time domain. It is then shown how ATP can be translated into a variant of timed graphs. This result allows the application of existing model-checking techniques to ATP. Finally, we propose a notion of hybrid systems as a generalization of timed graphs. Such systems can evolve, either by executing a discrete transition, or by performing some "continuous " transformation. The formalisms studied admit the same class of models: time deterministic and time continuous, possibly infinitely branching transition systems labeled by actions or durations.

. We propose a structural operational semantics that expresses temporal aspects of mobile and distributed systems, each sequential component of which has its local clock. Since the run-time support of a programming language implements the operations of the language via some lower-level routines, the same action, put in different contexts, may have different durations. Also the network topology affects these durations, typically when messages are exchanged. We model this through a transition system labelled by actions and their costs, in a discrete time. Then, we define two performance preordings that say when the execution of a process is faster than that of another. The first preorder is similar to those presented in the literature, while the second refines it in that it considers a process faster than another if it is such from some point onwards of its execution. Finally, as an example we compare the performance of a conventional uniprocessor architecture with a prefetch pipeline ar...