Probabilistic and prioritized models of timed CSP

Abstract

In this paper we present two languages that are refinements of timed CSP (Davies and Schneider, this volume): a probabilistic language, and a fully deterministic language with a notion of priority. In the first part of the paper we describe the deterministic language and its semantic model. The syntax is based upon that of timed CSP except some of the operators are refined so as to remove all nondeterminism; this produces prioritized operators. The semantics for our language represents a process as the set of possible behaviours for the process, where a behaviour models the priorities for different actions. A number of algebraic laws for our language are given and the model is illustrated with two examples. In the second part of the paper, we extend the language by adding a probabilistic choice operator. We produce a semantic model for our language which gives the probabilities of different behaviours occurring, as well as modelling the relative priorities for events within a behaviour. The model is illustrated with an example of a communications protocol transmitting messages over an unreliable medium.