Ergodic Theory of Stochastic Petri Networks

Baccelli, Francois

Ann. Probab., Tome 20 (1992) no. 4, p. 375-396 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1992-01-14
Classification:  Discrete event systems,  stochastic Petri networks,  event graphs,  queuing networks,  stationary processes,  stability,  stochastic recursive sequences,  subadditive ergodic theory,  multiplicative ergodic theory,  05C20,  60F20,  60G10,  60G17,  60G55,  60K25,  68Q75,  68Q90,  68R10,  93D05,  93E03,  93E15