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Stochastic Process Algebra, Reversed Processes and Product-Forms

Peter G. Harrison

Conference or Workshop Paper
17th International Symposium On Computer and Information Sciences (ISCIS 2002)
October, 2002

The Stochastic Process Algebra (SPA) formalism for performance models of communicating systems is briefly reviewed, focussing on the subset of Markovian Process Algebra (MPA). MPA facilitates analytical solutions for equilibrium state probabilities, in principle, but direct methods are severely limited by the size of the state space. By considering the reversed process of a stationary Markov chain, product-forms are derived for the equilibrium state probabilities in stochastic networks defined by a collection of cooperating MPA agents. Key to the analysis is the property of compositionality. Under quite general conditions, the well known product-forms for networks of queues (Jackson's theorem) and G-networks (with both positive and negative customers) can be simply obtained. Two new product forms are also derived by systematically following this mechanical approach.

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