Fayolle, G.; Malyshev, V. A.; Menshikov, M. V.; Sidorenko, A. F. Lyapounov functions for Jackson networks. (English) Zbl 0789.60078 Math. Oper. Res. 18, No. 4, 916-927 (1993). 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. Cited in 4 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:Lyapunov functions; Markovian Jackson networks; product form; stationary distribution PDFBibTeX XMLCite \textit{G. Fayolle} et al., Math. Oper. Res. 18, No. 4, 916--927 (1993; Zbl 0789.60078) Full Text: DOI Link