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Compositional Markovian Modelling Using a Process Algebra

In: Computations with Markov Chains

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  • Jane Hillston

    (University of Edinburgh)

Abstract

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.

Suggested Citation

  • Jane Hillston, 1995. "Compositional Markovian Modelling Using a Process Algebra," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 12, pages 177-196, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_12
    DOI: 10.1007/978-1-4615-2241-6_12
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