Detecting reversibility in Markovian Process Algebras

Abstract

A methodology is developed to determine when a process defined in terms of a Markovian Process Algebra is a reversible Markov process and so has a product form solution. In particular, we show how to detect birth-death processes, tree-like extensions of these and examine an approach to detecting more general reversible processes through the Kolmogorov criteria applied to a minimal state transition graph. Finally, we indicate how to exploit the compositionality of process algebras to detect more complex reversible, and other product-form, processes formed from interactions of simpler processes already known to be reversible.