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Mat. Tr., 2011, Volume 14, Number 1, Pages 3–49 (Mi mt205)  

This article is cited in 3 scientific papers (total in 3 papers)

Multitype branching processes with immigration in random environment, and polling systems

V. A. Vatutin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: For multitype branching processes with immigration evolving in a random environment and producing a final product, we find the tail distribution of the size of the final product accumulated in the process for a life period. Using this result, we investigate the tail distributions of the busy periods of the queueing polling systems of branching type with random service disciplines and random positive switch-over times.

Key words: subcritical branching processes with immigration, final product, random environment, limit theorems, polling systems, busy period.

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English version:
Siberian Advances in Mathematics, 2011, 21:1, 42–72

Bibliographic databases:

Document Type: Article
UDC: 519.2
Received: 29.04.2010

Citation: V. A. Vatutin, “Multitype branching processes with immigration in random environment, and polling systems”, Mat. Tr., 14:1 (2011), 3–49; Siberian Adv. Math., 21:1 (2011), 42–72

Citation in format AMSBIB
\Bibitem{Vat11}
\by V.~A.~Vatutin
\paper Multitype branching processes with immigration in random environment, and polling systems
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 3--49
\mathnet{http://mi.mathnet.ru/mt205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858652}
\elib{http://elibrary.ru/item.asp?id=16441654}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 1
\pages 42--72
\crossref{https://doi.org/10.3103/S1055134411010020}
\elib{http://elibrary.ru/item.asp?id=17002950}


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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. E. E. D'yakonova, “Multitype branching processes evolving in a Markovian environment”, Discrete Math. Appl., 22:5-6 (2012), 639–664  mathnet  crossref  crossref  mathscinet  elib
    2. Bansaye V., Camanes A., “Queueing For An Infinite Bus Line and Aging Branching Process”, Queueing Syst., 88:1-2 (2018), 99–138  crossref  mathscinet  zmath  isi  scopus
    3. Zerner M.P.W., “Recurrence and Transience of Contractive Autoregressive Processes and Related Markov Chains”, Electron. J. Probab., 23 (2018), 27  crossref  mathscinet  zmath  isi  scopus
  • Математические труды Siberian Advances in Mathematics
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