Abstract
We consider queueing networks which are made from servers exchanging their positions on a graph. When two servers exchange their positions, they take their customers with them. Each customer has a fixed destination. Customers use the network to reach their destinations, which is complicated by movements of the servers. We develop the general theory of such networks and establish the convergence of the symmetrized version of such a network to some nonlinear Markov process.
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Original Russian Text cF. Baccelli, A.N. Rybko, S.B. Shlosman, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 2, pp. 85–110.
The International Dobrushin Prize for 2015 was awarded to Alexander Nikolaevich Rybko. The prize was presented on July 21, 2015, at Sinai’s seminar of the Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences.
The results of Sections 3–5 were obtained at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.
Supported in part by the Labex Archimede (ANR-11-LABX-0033) and the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR).
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Baccelli, F., Rybko, A.N. & Shlosman, S.B. Queueing networks with mobile servers: The mean-field approach. Probl Inf Transm 52, 178–199 (2016). https://doi.org/10.1134/S0032946016020071
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DOI: https://doi.org/10.1134/S0032946016020071