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Problemy Peredachi Informatsii, 1998, Volume 34, Issue 4, Pages 76–108 (Mi ppi426)  

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

Large Systems

Large Deviations for Random Processes with Independent Increments on Infinite Intervals

R. L. Dobrushin, E. A. Pechersky
References:
Abstract: Methods developed in the theory of large deviations are an appropriate tool for investigation of probabilities of large fluctuations in queueing systems. In the paper, the large-deviation principle for generalized Poisson processes defined on the positive half-line $[0,\infty)$ is proved. Our approach is to find a representation of a parameter of the queueing system under investigation in terms of input flows of the system. Then the probabilities of large fluctuations of this parameter can be examined if the large-deviation principle for input processes is proved. With the help of the large-deviation principle proved here, we give a new proof for the known result on the asymptotics of the logarithm of the probability of large delay in a queueing system with a single server and Poisson input flow.
Received: 12.08.1997
Bibliographic databases:
Document Type: Article
UDC: 621.391.1:519.2
Language: Russian
Citation: R. L. Dobrushin, E. A. Pechersky, “Large Deviations for Random Processes with Independent Increments on Infinite Intervals”, Probl. Peredachi Inf., 34:4 (1998), 76–108; Problems Inform. Transmission, 34:4 (1998), 354–382
Citation in format AMSBIB
\Bibitem{DobPec98}
\by R.~L.~Dobrushin, E.~A.~Pechersky
\paper Large Deviations for Random Processes with Independent Increments on Infinite Intervals
\jour Probl. Peredachi Inf.
\yr 1998
\vol 34
\issue 4
\pages 76--108
\mathnet{http://mi.mathnet.ru/ppi426}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1793496}
\zmath{https://zbmath.org/?q=an:0935.60073}
\transl
\jour Problems Inform. Transmission
\yr 1998
\vol 34
\issue 4
\pages 354--382
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  • https://www.mathnet.ru/eng/ppi426
  • https://www.mathnet.ru/eng/ppi/v34/i4/p76
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы передачи информации Problems of Information Transmission
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