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Semi-Product-Form Solution for Models with State-Dependent Rates

Nigel Thomas, Andrea Marin, Peter G. Harrison

Conference or Workshop Paper
9th Workshop on Process Algebra and Stochastically Timed Activities (PASTA 2010)
August, 2010

In this paper we consider the problem of finding a decomposed solution to a Markov model where the action rates may depend on the global state space. To do this we consider regular cycles in the underlying state space and show that a semi-product form solution exists when the functions describing the action rates have specific forms. The approach is illustrated with a simple queueing example although it clearly extends to more general cases. The results for semi-product form solutions are not entirely new, however the method by which they are derived is both novel and intuitive.

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