Using Markovian Process Algebra to Specify Interactions in Queueing Systems

The advantages of using stochastic process algebra to specify performance models are well-documented. There remains, however, a reluctance in some quarters to use process algebras; this is particularly the case amongst queueing theorists. This paper demonstrates the use of a Markovian process algebra to represent a wide range of queueing models. Moreover, it shows that the most common interactive behaviours found in queueing systems can be modelled simply in a Markovian process algebra, and discusses how such specifications can lead to an automated numerical solution method. An additional objective of this work is to specify queueing models in a form which facilitates efficient solution techniques. It is intended that characterising the syntactic forms within the Markovian process algebra which give rise to these efficient solution methods will subsequently allow the methods to be applied to a much wider range of models specified in the process algebra.