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Probl. Peredachi Inf., 2000, Volume 36, Issue 2, Pages 69–95 (Mi ppi478)  

This article is cited in 9 scientific papers (total in 10 papers)

Communication Network Theory

Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks

F. I. Karpelevich, A. N. Rybko


Abstract: We study the thermodynamical limit for a mean-field model describing how a closed symmetric queueing network operates. The Markov process under consideration is invariant under the action of a certain symmetry group $G$ in the phase space. We prove that the quotient process on the space of orbits of the $G$-action converges to a limit deterministic dynamical system.

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English version:
Problems of Information Transmission, 2000, 36:2, 154–179

Bibliographic databases:
UDC: 621.391.1:519.2
Received: 11.08.1999

Citation: F. I. Karpelevich, A. N. Rybko, “Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks”, Probl. Peredachi Inf., 36:2 (2000), 69–95; Problems Inform. Transmission, 36:2 (2000), 154–179

Citation in format AMSBIB
\Bibitem{KarRyb00}
\by F.~I.~Karpelevich, A.~N.~Rybko
\paper Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks
\jour Probl. Peredachi Inf.
\yr 2000
\vol 36
\issue 2
\pages 69--95
\mathnet{http://mi.mathnet.ru/ppi478}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1763582}
\zmath{https://zbmath.org/?q=an:0967.60096}
\transl
\jour Problems Inform. Transmission
\yr 2000
\vol 36
\issue 2
\pages 154--179


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. È. B. Vinberg, I. M. Gel'fand, S. G. Gindikin, E. B. Dynkin, V. A. Malyshev, R. A. Minlos, A. L. Onishchik, I. I. Pyatetskii-Shapiro, A. N. Rybko, Yu. M. Sukhov, S. B. Shlosman, “Fridrikh Israilevich Karpelevich (obituary)”, Russian Math. Surveys, 56:1 (2001), 141–147  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Malyshev, S. A. Pirogov, A. N. Rybko, “Random walks and chemical networks”, Mosc. Math. J., 4:2 (2004), 441–453  mathnet  crossref  mathscinet  zmath
    3. A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. I”, Mosc. Math. J., 5:3 (2005), 679–704  mathnet  crossref  mathscinet  zmath
    4. A. N. Rybko, S. B. Shlosman, “Poisson hypothesis for information networks. II”, Mosc. Math. J., 5:4 (2005), 927–959  mathnet  crossref  mathscinet  zmath
    5. A. N. Rybko, S. B. Shlosman, “Poisson Hypothesis: Combinatorial Aspect”, Problems Inform. Transmission, 41:3 (2005), 230–236  mathnet  crossref  mathscinet  zmath
    6. A. A. Sergeev, “Limit theorems for one class of Polling models”, Theory Probab. Appl., 50:3 (2006), 510–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. 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
    8. 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
    9. 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
    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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