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Lyapounov functions for Jackson networks. (English) Zbl 0789.60078

Summary: We construct explicitly Lyapunov functions for Markovian Jackson networks. Two direct corollaries are obtained: first a proof of necessary and sufficient conditions for ergodicity, without using the famous Jackson’s product form; secondly, an exponential convergence rate to the stationary distribution. We also consider small perturbations of the transition probabilities (yielding thus non-Jackson networks) and prove that the corresponding stationary distribution is an analytic function of these perturbations.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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