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Structured characterization of the Markov chain of phase-type SPN.

Donatelli, S.; Haddad, S.; Moreaux, P.

In: Lecture Notes in Computer Science, Vol. 1469: Computer Performance Evaluation, pages 243-254. Springer-Verlag, 1998.

Abstract: This paper presents a characterization of the Markovian state space of a stochastic Petri net with phase-type distributed transitions as a union of Cartesian products of a set of `components' of the net. The method uses an abstract of the net based on the vectors of enabling degrees of phase-type transitions, as well as on the sets of `interrupted clients'. Following the decomposition used for the state space characterization, a tensor algebra expression for the infinitesimal generator (actually for its rate matrix) is given, that allows the steady-state probability to be computed directly from a set of matrices of the size of the components, without the need of storing the whole infinitesimal generator.

Keywords: Markov chains, phase-type distributions, stochastic Petri nets, structural characterization.

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