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Generalization of queueing network product form solutions to stochastic Petri nets

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2 Author(s)
G. Florin ; Centre d'Etudes et de Recherche en Inf. du CNAM, Paris, France ; S. Natkin

A new solution is given for the steady-state probability computation of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (a bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). It is shown that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form using matrix and vectors instead of scalars. A prototype solver developed from this result is presented

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IEEE Transactions on Software Engineering  (Volume:17 ,  Issue: 2 )