Modelling Network Performance with a Spatial Stochastic Process Algebra

This paper shows how network performance can be modeled by a stochastic process algebra which includes spatial concepts. The concepts are added to PEPA and the motivation is that location of actions or processes with respect to other parts of a system may affect the time taken by an event. First a very general spatial stochastic process algebra is presented. Locations are introduced to both actions and processes, and are provided with weighted directed graph or hypergraph structure. This general process algebra is then made more concrete to illustrate its use in a networking context. It is shown how analyses based on continuous time Markov chains (CTMCs) can be expressed in terms of the directed graphs used in the concrete process algebra.