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Probl. Peredachi Inf., 2000, Volume 36, Issue 1, Pages 26–47 (Mi ppi468)  

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

Communication Network Theory

Nonergodicity of a Queueing Network under Nonstability of Its Fluid Model

A. A. Pukhal'skii, A. N. Rybko


Abstract: We study ergodicity properties of open queueing networks for which the associated fluid models have trajectories that go to infinity. It is proved that if a trajectory is stable in a certain sense and grows to infinity linearly, then the underlying stochastic process is nonergodic. The result applies to the basic nontrivial examples of nonergodic networks found by Bramson, and Rybko and Stolyar. The proof employs some general results from the large deviation theory.

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English version:
Problems of Information Transmission, 2000, 36:1, 23–41

Bibliographic databases:
UDC: 621.395.74:519.27
Received: 18.01.1999

Citation: A. A. Pukhal'skii, A. N. Rybko, “Nonergodicity of a Queueing Network under Nonstability of Its Fluid Model”, Probl. Peredachi Inf., 36:1 (2000), 26–47; Problems Inform. Transmission, 36:1 (2000), 23–41

Citation in format AMSBIB
\Bibitem{PukRyb00}
\by A.~A.~Pukhal'skii, A.~N.~Rybko
\paper Nonergodicity of a~Queueing Network under Nonstability of Its Fluid Model
\jour Probl. Peredachi Inf.
\yr 2000
\vol 36
\issue 1
\pages 26--47
\mathnet{http://mi.mathnet.ru/ppi468}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1746007}
\zmath{https://zbmath.org/?q=an:0966.60095}
\transl
\jour Problems Inform. Transmission
\yr 2000
\vol 36
\issue 1
\pages 23--41


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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. K. M. Khanin, D. V. Khmelev, A. N. Rybko, A. A. Vladimirov, “Steady solutions for FIFO networks”, Mosc. Math. J., 1:3 (2001), 407–419  mathnet  crossref  mathscinet  zmath
    2. Dantzer, JF, “Fluid limits of string valued Markov processes”, Annals of Applied Probability, 12:3 (2002), 860  crossref  mathscinet  zmath  isi
    3. Dai, JG, “Stability and instability of a two-station queueing network”, Annals of Applied Probability, 14:1 (2004), 326  crossref  mathscinet  zmath  isi
    4. A. P. Kovalevskii, V. A. Topchii, S. G. Foss, “On Stability of a Queueing System with Continuum Branching Fluid Limits”, Problems Inform. Transmission, 41:3 (2005), 254–279  mathnet  crossref  mathscinet  zmath
    5. Gamarnik, D, “Instability in stochastic and fluid queueing networks”, Annals of Applied Probability, 15:3 (2005), 1652  crossref  mathscinet  zmath  isi
    6. Yildirim, U, “Stability in queueing networks via the finite decomposition property”, Asia-Pacific Journal of Operational Research, 25:3 (2008), 393  crossref  mathscinet  zmath  isi
    7. S. V. Anulova, “Approximation of initial loading of infinite-server systems”, Autom. Remote Control, 69:7 (2008), 1154–1161  mathnet  crossref  mathscinet  zmath  isi
    8. Rybko, A, “Spontaneous Resonances and the Coherent States of the Queuing Networks”, Journal of Statistical Physics, 134:1 (2009), 67  crossref  mathscinet  zmath  adsnasa  isi
    9. Gamarnik D., Katz D., “On Deciding Stability of Multiclass Queueing Networks Under Buffer Priority Scheduling Policies”, Ann Appl Probab, 19:5 (2009), 2008–2037  crossref  mathscinet  zmath  isi
    10. Schoenlein M., Wirth F., “On converse Lyapunov theorems for fluid network models”, Queueing Syst, 70:4 (2012), 339–367  crossref  mathscinet  zmath  isi
  • Проблемы передачи информации Problems of Information Transmission
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