Ergodic Theorems for Stochastic Operators and Discrete Event Networks

François Baccelli (1) , Jean Mairesse (1)

1 MISTRAL - Modeling of Computer Systems and Telecommunication Networks : Research and Software Development

We present a survey of the main ergodic theory techniques which are used in the study of iterates of monotone and homogeneous stochastic operators. It is shown that ergodic theorems on discrete event networks (queueing networks and/or Petri nets) are a generalization of these stochastic operator theorems. Kingman's subadditive ergodic Theorem is the key tool for deriving what we call first order ergodic results. We also show how to use backward constructions (also called Loynes schemes in network theory) in order to obtain second order ergodic results. We propose a review of systems entering the framework insisting on two models, precedence constraints networks and Jackson type networks

Mots clés: Queueing network; Petri net; subadditive ergodic theory; Loynes scheme; stochastic recursive sequences.; stochastic recursive sequences

Domaines: Autre [cs.OH]

François Baccelli, Jean Mairesse. Ergodic Theorems for Stochastic Operators and Discrete Event Networks. Cambridge University Press. Idempotency, Cambridge University Press, pp.171-208, 1998, Publications of the Newton Institute, 0 521 55344. ⟨inria-00074049v2⟩