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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

O. P. Vinogradov

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:

Received: 30.01.1967

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}


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