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Poisson Hypothesis for information networks (A study in non-linear Markov processes)

Alexander Rybko·Senya Shlosman
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Abstract

In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov processes, have a line of fixed points which are global attractors. To do this we derive the corresponding non-linear integral equation and we explore its self-averaging properties. Our derivation relies on a solution of a combinatorial problem of rode placements.

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Alexander Rybko, Senya Shlosman. 2003-03-04. Poisson Hypothesis for information networks (A study in non-linear Markov processes). https://arxiv.org/abs/math-ph/0303010

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