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 Mosc. Math. J., 2017, Volume 17, Number 1, Pages 145–160 (Mi mmj630)

Poisson hypothesis for open networks at low load

A. Rybkoa, Senya Shlosmanbca, A. Vladimirova

a Inst. of the Information Transmission Problems, RAS, Moscow, Russia
b Skolkovo Institute of Science and Technology, Moscow, Russia
c Aix Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288, Marseille, France

Abstract: We study large communication networks of the mean-field type. The input flows to the nodes of the network are supposed to be stationary and with low rate. We show that such a network is ergodic, i.e., it goes to the stationary state, which does not depend on the initial state of the network. This is in contrast with the high load regime, when the large time behavior of the network might depend on its initial state. Our technique is based on the coupling construction, which couples two Non-Linear Markov Processes.

Key words and phrases: mean-field, non-linear Markov process, queuing theory.

 Funding Agency Grant Number Agence Nationale de la Recherche ANR-11-LABX-0033ANR-11-IDEX-0001-02 Russian Science Foundation 14-50-00150 Part of this work has been carried out in the framework of the Labex Archimede (ANR-11-LABX-0033) and of 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). Part of this work has been carried out at IITP RAS. The support of Russian Foundation for Sciences (project No. 14-50-00150) is gratefully acknowledged.

DOI: https://doi.org/10.17323/1609-4514-2017-17-1-145-160

Full text: http://www.mathjournals.org/.../2017-017-001-009.html
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MSC: 60J27
Received: June 10, 2015; in revised form July 8, 2016
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Citation: A. Rybko, Senya Shlosman, A. Vladimirov, “Poisson hypothesis for open networks at low load”, Mosc. Math. J., 17:1 (2017), 145–160

Citation in format AMSBIB
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