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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1968},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a19/
%G ru
%F TVP_1968_13_2_a19
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/