Stochastic Process Algebras: From Individuals to Populations

In this paper we report on progress in the use of stochastic process algebras for representing systems which contain many replications of components such as clients, servers and devices. Such systems have traditionally been difficult to analyse even when using high-level models because of the need to represent the vast range of their potential behaviour. Models of concurrent systems with many components very quickly exceed the storage capacity of computing devices even when efficient data structures are used to minimize the cost of representing each state. Here, we show how population-based models that make use of a continuous approximation of the discrete behaviour can be used to efficiently analyse the temporal behaviour of very large systems via their collective dynamics. This approach enables modellers to study problems that cannot be tackled with traditional discrete-state techniques such as continuous-time Markov chains.