Semi-numerical Solution of Stochastic Process Algebra Models
A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the complete global state space of the CTMC. The method works for a fixed number of sequential processes running in parallel and which all synchronize on the same global set of actions. The behaviour of the processes is expressed by the embedded Markov chain of a semi-Markov process and by distribution functions (exponomials) which describe the times between synchronizations. The solution method is exact, hence, the state space explosion problem for this class of processes has been solved. A distributed implementation of the solution technique is straightforward.
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