Compositional Markovian Modelling Using A Process Algebra

We introduce a stochastic process algebra, PEPA, as a high-level modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model. Recent extensions of these algebras, associating random variables with actions, make the models also amenable to Markovian analysis. A compositional structure is inherent in the PEPA language. As well as the clear advantages that this offers for model construction, we demonstrate how this compositionality may be exploited to reduce the state space of the CTMC. This leads to an exact aggregation based on lumpability. Moreover this technique, taking advantage of symmetries within the system, may be formally defined in terms of the PEPA description of the model. An equivalence relation, strong equivalence, developed as a process algebra bisimulation relation, is used to partition the derivation graph.