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January, 1992 Ergodic Theory of Stochastic Petri Networks
Francois Baccelli
Ann. Probab. 20(1): 375-396 (January, 1992). DOI: 10.1214/aop/1176989932

Abstract

Stochastic Petri networks provide a general formalism for describing the dynamics of discrete event systems. The present paper focuses on a subclass of stochastic Petri networks called stochastic event graphs, under the assumption that the variables used for their "timing" form stationary and ergodic sequences of random variables. We show that such stochastic event graphs can be seen as a $(\max, +)$ linear system in a random, stationary and ergodic environment. We then analyze the associated Lyapounov exponents and construct the stationary and ergodic regime of the increments, by proving an Oseledec-type multiplicative ergodic theorem. Finally, we show how to construct the stationary marking process from these results.

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Francois Baccelli. "Ergodic Theory of Stochastic Petri Networks." Ann. Probab. 20 (1) 375 - 396, January, 1992. https://doi.org/10.1214/aop/1176989932

Information

Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0742.60091
MathSciNet: MR1143426
Digital Object Identifier: 10.1214/aop/1176989932

Subjects:
Primary: 05C20‎
Secondary: 60F20 , 60G10 , 60G17 , 60G55 , 60K25 , 68Q75 , 68Q90 , 68R10 , 93D05 , 93E03 , 93E15

Keywords: discrete event systems , event graphs , multiplicative ergodic theory , queuing networks , stability , Stationary processes , stochastic Petri networks , stochastic recursive sequences , subadditive ergodic theory

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 1 • January, 1992
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