Stationary ergodic Jackson networks: results and counter-examples

F. Baccelli · Sergey Foss · Jean Mairesse

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

Abstract 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.

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References

1994Stability, queue length, and delay of deterministic and stochastic queueing networks 2004Jobshop-Like Queueing Systems 1967Closed Queuing Systems with Exponential Servers 1994Stability of Generalized Jackson Networks 1990A paradox of congestion in a queuing network 1990The stability of open queueing networks 1992Stationary Stochastic Models.1995On the saturation rule for the stability of queues

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2004Cyclic queueing networks with subexponential service times

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