Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 366-375
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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/
@article{TVP_1968_13_2_a19,
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/}
}
TY - JOUR
AU - O. P. Vinogradov
TI - The problem of the distribution of the maximal queue size and its application
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1968
SP - 366
EP - 375
VL - 13
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a19/
LA - ru
ID - TVP_1968_13_2_a19
ER -
%0 Journal Article
%A O. P. Vinogradov
%T The problem of the distribution of the maximal queue size and its application
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1968
%P 366-375
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a19/
%G ru
%F TVP_1968_13_2_a19
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.
