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Pré-Publication, Document De Travail Année : 2003

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

Résumé

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.

Dates et versions

hal-00126999 , version 1 (27-01-2007)

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Alexander Rybko, Senya Shlosman. Poisson Hypothesis for information networks (A study in non-linear Markov processes). 2003. ⟨hal-00126999⟩
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