Abstract
This paper presents a characterization of the Markovian state space of a Stochastic Petri Nets with phase-type distribution transitions as a union of Cartesian products of a set of “components” of the net. The method uses an abstract view 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.
This work has been developed within the project HCM CT94-0452 (MATCH) of the European Union. At time of writing S. Donatelli was visiting professor at Lamsade, at the University of Paris-Dauphine.
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Donatelli, S., Haddad, S., Moreaux, P. (1998). Structured Characterization of the Markov Chain of Phase-Type SPN. In: Puigjaner, R., Savino, N.N., Serra, B. (eds) Computer Performance Evaluation. TOOLS 1998. Lecture Notes in Computer Science, vol 1469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68061-6_20
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