Abstract
The paper is devoted to the computation of stationary distributions of queueing systems in random media. Results obtained for considered models follow from a theorem proved in the paper. As an application of the theorem, we consider Jackson networks whose structure (the set of working nodes, service and input flow intensities, routing matrix, state set) and type (open/closed network) varies as the state of another network or of the environment changes. Product-form formulas for the computation of stationary distributions of the considered networks are obtained, and algorithms for the solution of auxiliary problems are developed.
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Ivchenko, G.I., Kashtanov, V.A., and Kovalenko, I.N., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Vyssh. Shkola, 1982.
Basharin, G.P. and Tolmachev, A.L., Queueing Network Theory and Its Applications to the Analysis of Information-Computing Networks, in Itogi Nauki Tekh. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., vol. 21, Moscow: VINITI, 1983, pp. 3–119.
Tsitsiashvili, G.Sh. and Osipova, M.A., New Product Theorems for Queueing Networks, Probl. Peredachi Inf., 2005, vol. 41, no. 2, pp. 111–122 [Probl. Inf. Trans. (Engl. Transl.), 2005, vol. 41, no. 2, pp. 171–181].
Serfozo, R., Introduction to Stochastic Networks, New York: Springer, 1999.
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Original Russian Text © G.Sh. Tsitsiashvili, M.A. Osipova, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, pp. 101–108.
Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00512a.
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Tsitsiashvili, G.S., Osipova, M.A. Probability distribution in varying-structure queueing networks. Probl Inf Transm 42, 158–165 (2006). https://doi.org/10.1134/S0032946006020098
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DOI: https://doi.org/10.1134/S0032946006020098