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Estimates of Cycle Times in Stochastic Petri Nets.

Baccelli, F.; Konstantopoulos, P.

In: Rapport de recherche 1572, INRIA, Rocquencourt. 1992.

Abstract: This paper focuses on the derivation of bounds and estimates for cycle times of strongly connected stochastic event graphs with i.i.d. holding times. We use association properties satisfied by partial sums of the holding times in order to prove that the firing epochs compare for stochastic ordering with the last birth in a multitype branching process, the structure of which is determined from the characteristics of the event graph using simple algebraic manipulations. Classical large deviation estimates are then used to compute the growth rate of this last birth epoch, following the method of Kingman and Biggins. The method allows one to derive a computable upper bound for the cycle time, and is exemplified on tandam queuing networks with communication blocking.

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