Deriving Mean Field Equations from Large Process Algebra Models

Abstract

In many domain areas the behaviour of a system can be described at two levels: the behaviour of individual components, and the behaviour of the system as a whole. Often deriving one from the other is impossible, or at least intractable, especially when realistically large systems are considered. Here we present a rigorous algorithm which, given an individual based model in the process algebra WSCCS describing the components of a system and the way they interact, can produce a system of mean field equations which describe the mean behaviour of the system as a whole. This transformation circumvents the state explosion problem, allowing us to handle systems of any size by providing an approximation of the system behaviour. From the mean field equations we can investigate the transient dynamics of the system. This approach was motivated by problems in biological systems, but is applicable to distributed systems in general.