2004/06/07 by Alexander Rybko, A. Rybko, Rybko, A. +3 · 1 citation
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/0406110
77 pages
arxiv created 2004/06/07 · openalex publication_date 2004/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system, defined by the non-linear Markov process, has a line of fixed points which are global attractors. To do this we derive the corresponding non-linear equation and we explore its self-averaging properties. We also argue that in cases of havy-tail service times the PH can be violated.