2003/03/04 by Alexander Rybko, Rybko, Alexander, Senya Shlosman +1
Mathematics · Physics and Astronomy · #60J25 #82C20 #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60J25 #msc:82C20
paper · pdf · doi:10.48550/arxiv.math-ph/0303010
70 pages
arxiv created 2003/03/04 · openalex publication_date 2003/03/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.