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Moscow Mathematical Journal, 2005, Volume 5, Number 4, Pages 927–959
DOI: https://doi.org/10.17323/1609-4514-2005-5-4-927-959 (Mi mmj229) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Poisson hypothesis for information networks. II

A. N. Rybkoa, S. B. Shlosmanb

a Institute for Information Transmission Problems, Russian Academy of Sciences
b CNRS – Center of Theoretical Physics
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DOI: https://doi.org/10.17323/1609-4514-2005-5-4-927-959
Abstract: This is the second part of our paper. We study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queuing 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 heavy-tail service times the PH can be violated.
Key words and phrases: Mean-field models, server, waiting time, phase transition, limit theorem, self-averaging property, attractor.
Received: June 14, 2005
Bibliographic databases:
MSC: Primary 82C20; Secondary 60J25
Language: English
Citation: A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. II”, Mosc. Math. J., 5:4 (2005), 927–959
Citation in format AMSBIB
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\by A.~N.~Rybko, S.~B.~Shlosman
\paper Poisson hypothesis for information networks.~II
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 4
\pages 927--959
\mathnet{http://mi.mathnet.ru/mmj229}
\crossref{https://doi.org/10.17323/1609-4514-2005-5-4-927-959}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2267315}
\zmath{https://zbmath.org/?q=an:1126.60077}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208595600012}
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