Real-Time Behaviour of Asynchronous Agents

In this paper, we present a calculus for real-time communicating systems. The calculus is an extension of Milner's CCS with explicit time. In SCCS, Open image in new window means that if P exists at time r, it will proceed to Q at time r + 1. The time delay is exactly one unit. We extend this idea to asynchronous agents by allowing arbitrary delays. We write Open image in new window to mean that aftert units of time, P will become Q, where e stands for idling. Based on the notion of bisimulation, two equivalence relations over agents are defined. It has been shown that the strong equivalence is a congruence and the weak one is preserved by all operators except summation and recursion [W90]. Various examples are given to illustrate the approach.