Stationary ergodic Jackson networks: results and counter-examples

François Baccelli (1) , Serguei Foss (2) , Jean Mairesse (3)

1 MISTRAL - Modeling of Computer Systems and Telecommunication Networks : Research and Software Development
2 Sobolev Institute of Mathematics
3 BRIMS - Basic Research Institute in Mathematical Sciences

This paper gives a survey of recent results on generalized Jackson networks, where classical exponential or i.i.d. assumptions on services and routings are replaced by stationary and ergodic assumptions. We first show that the most basic features of the network may exhibit unexpected behavior. Several probabilistic properties are then discussed, including a strong law of large numbers for the number of events in the stations, the existence, uniqueness and representation of stationary regimes for queue size and workload.

Mots clés: Jackson network; Jackson network.

Domaines: Mathématique discrète [cs.DM]

François Baccelli, Serguei Foss, Jean Mairesse. Stationary ergodic Jackson networks: results and counter-examples. Stochastic Networks: Theory and Applications, Oxford University Press, pp.281-307, 1996. ⟨hal-00165920⟩