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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 2, Pages 446–450
DOI: https://doi.org/10.4213/tvp779 (Mi tvp779) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Limit theorems on maximums of Poisson sequences and their applications to queuing theory

A. V. Lebedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (314 kB) Citations (2)
DOI: https://doi.org/10.4213/tvp779
Abstract: We consider a sequence of independent Poisson random variables $X_n$ with parameters $\lambda_n$. Asymptotic properties of maximums $Y_n=\max_{1\le i\le n}X_i$ under the dependence on properties of the sequence $\{\lambda_n\}$ are studied. The results obtained are applied to investigating the maximal number of claims in the system $M|G|\infty$ with parameters dependent on time.
Keywords: Poisson random variables, maximums, limit theorems, almost sure convergence, infinitely linear queuing systems.
Received: 04.11.1996
Revised: 21.10.1998
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 2, Pages 400–404
DOI: https://doi.org/10.1137/S0040585X97977641
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Lebedev, “Limit theorems on maximums of Poisson sequences and their applications to queuing theory”, Teor. Veroyatnost. i Primenen., 44:2 (1999), 446–450; Theory Probab. Appl., 44:2 (2000), 400–404
Citation in format AMSBIB
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\by A.~V.~Lebedev
\paper Limit theorems on maximums of Poisson sequences and their applications to queuing theory
\jour Teor. Veroyatnost. i Primenen.
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\issue 2
\pages 446--450
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\zmath{https://zbmath.org/?q=an:0973.60056}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 2
\pages 400--404
\crossref{https://doi.org/10.1137/S0040585X97977641}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000089405200013}
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  • https://www.mathnet.ru/eng/tvp779
  • https://doi.org/10.4213/tvp779
  • https://www.mathnet.ru/eng/tvp/v44/i2/p446
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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