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Mosc. Math. J., 2005, Volume 5, Number 3, Pages 679–704 (Mi mmj215)  

This article is cited in 10 scientific papers (total in 10 papers)

Poisson hypothesis for information networks. I

A. N. Rybkoa, S. B. Shlosmanb

a Institute for Information Transmission Problems, Russian Academy of Sciences
b CNRS – Center of Theoretical Physics

Abstract: In this 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.

DOI: https://doi.org/10.17323/1609-4514-2005-5-3-679-704

Full text: http://www.ams.org/.../abst5-3-2005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 82C20; Secondary 60J25
Received: June 14, 2005
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Citation: A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. I”, Mosc. Math. J., 5:3 (2005), 679–704

Citation in format AMSBIB
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\by A.~N.~Rybko, S.~B.~Shlosman
\paper Poisson hypothesis for information networks.~I
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 3
\pages 679--704
\mathnet{http://mi.mathnet.ru/mmj215}
\crossref{https://doi.org/10.17323/1609-4514-2005-5-3-679-704}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2241817}
\zmath{https://zbmath.org/?q=an:1111.82034}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595500011}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. A. A. Vladimirov, A. N. Rybko, S. B. Shlosman, “Self-averaging Property of Queueing Systems”, Problems Inform. Transmission, 42:4 (2006), 344–355  mathnet  crossref  mathscinet
    2. A. A. Zamyatin, V. A. Malyshev, A. D. Manita, “Homeostasis in chemical reaction pathways”, Theory Probab. Appl., 51:4 (2007), 714–723  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. N. D. Vvedenskaya, Yu. M. Suhov, “Multiuser Multiple-Access System: Stability and Metastability”, Problems Inform. Transmission, 43:3 (2007), 263–269  mathnet  crossref  mathscinet  zmath  isi
    4. A. N. Rybko, S. B. Shlosman, “Phase transitions in the queuing networks and the violation of the Poisson hypothesis”, Mosc. Math. J., 8:1 (2008), 159–180  mathnet  crossref  mathscinet  zmath
    5. Rybko A., Shlosman S., Vladimirov A., “Spontaneous resonances and the coherent states of the queuing networks”, J. Stat. Phys., 134:1 (2009), 67–104  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Muzychka S.A., Vaninsky K.L., “A Class of Nonlinear Random Walks Related to the Ornstein–Uhlenbeck Process”, Markov Processes and Related Fields, 17:2 (2011), 277–304  mathscinet  zmath  isi
    7. S. A. Muzychka, “A class of nonlinear processes admitting complete study”, Moscow University Mathematics Bulletin, 70:3 (2015), 141–143  mathnet  crossref  mathscinet  isi
    8. F. Baccelli, A. N. Rybko, S. B. Shlosman, “Queueing networks with mobile servers: the mean-field approach”, Problems Inform. Transmission, 52:2 (2016), 178–199  mathnet  crossref  mathscinet  isi  elib
    9. A. Rybko, Senya Shlosman, A. Vladimirov, “Poisson hypothesis for open networks at low load”, Mosc. Math. J., 17:1 (2017), 145–160  mathnet  crossref  mathscinet
    10. A. A. Vladimirov, S. A. Pirogov, A. N. Rybko, S. B. Shlosman, “Propagation of chaos and Poisson hypothesis”, Problems Inform. Transmission, 54:3 (2018), 290–299  mathnet  crossref  isi  elib
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