Generalization of Queueing Network Product Form Solutions to Stochastic Petri Nets

Authors:
Gerard Florin;Stéphane Natkin
Affiliations:
CEDRIC, Paris, France;CEDRIC, Paris, France
Venue:
IEEE Transactions on Software Engineering
Year:
1991

Citing 5
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Abstract

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.