Geodesic
The problem of the distribution of the maximal queue size and its application
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 366-375 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {O. P. Vinogradov},
     title = {The problem of the distribution of the maximal queue size and its application},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {366--375},
     year = {1968},
     volume = {13},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a19/}
}
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O. P. Vinogradov. The problem of the distribution of the maximal queue size and its application. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 366-375. http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a19/