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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 2, Pages 366–375 (Mi tvp859)

Short Communications

The problem of the distribution of the maximal queue size and its application

Moscow

Abstract: In this paper we deal with the system $GI/M/1$. Let $\tau_n$ be the first time when the size of the queue equals $n$. An expression for $\mathbf Me^{-s\tau}n$ is obtained and the asymptotic behaviour of $\mathbf M\tau_n$ as $n\to\infty$ is studied. We prove also limit theorems for $\tau_n/\mathbf M\tau_n$ ($n\to\infty$). These results enable to analyse the system which has at most $n$ customers simultaneously.

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English version:
Theory of Probability and its Applications, 1968, 13:2, 346–353

Bibliographic databases:

Citation: O. P. Vinogradov, “The problem of the distribution of the maximal queue size and its application”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 366–375; Theory Probab. Appl., 13:2 (1968), 346–353

Citation in format AMSBIB
\Bibitem{Vin68} \by O.~P.~Vinogradov \paper The problem of the distribution of the maximal queue size and its application \jour Teor. Veroyatnost. i Primenen. \yr 1968 \vol 13 \issue 2 \pages 366--375 \mathnet{http://mi.mathnet.ru/tvp859} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=237020} \zmath{https://zbmath.org/?q=an:0167.46702|0165.19904} \transl \jour Theory Probab. Appl. \yr 1968 \vol 13 \issue 2 \pages 346--353 \crossref{https://doi.org/10.1137/1113045}