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Matematicheskie Trudy, 2011, Volume 14, Number 1, Pages 3–49 (Mi mt205)  
This article is cited in 15 scientific papers (total in 15 papers)

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

V. A. Vatutin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (402 kB) Citations (15)
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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.
Received: 29.04.2010
English version:
Siberian Advances in Mathematics, 2011, Volume 21, Issue 1, Pages 42–72
DOI: https://doi.org/10.3103/S1055134411010020
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
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{https://mathscinet.ams.org/mathscinet-getitem?mr=2858652}
\elib{https://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{https://elibrary.ru/item.asp?id=17002950}
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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