Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 541-546
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O. P. Vinogradov. Limiting distribution for the moment of first loss of a customer in a single-line service system with a limited number of positions in the queue. Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 541-546. http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/
@article{MZM_1968_3_5_a6,
author = {O. P. Vinogradov},
title = {Limiting distribution for the moment of first loss of a~customer in a~single-line service system with a~limited number of positions in the queue},
journal = {Matemati\v{c}eskie zametki},
pages = {541--546},
year = {1968},
volume = {3},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/}
}
TY - JOUR
AU - O. P. Vinogradov
TI - Limiting distribution for the moment of first loss of a customer in a single-line service system with a limited number of positions in the queue
JO - Matematičeskie zametki
PY - 1968
SP - 541
EP - 546
VL - 3
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/
LA - ru
ID - MZM_1968_3_5_a6
ER -
%0 Journal Article
%A O. P. Vinogradov
%T Limiting distribution for the moment of first loss of a customer in a single-line service system with a limited number of positions in the queue
%J Matematičeskie zametki
%D 1968
%P 541-546
%V 3
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/
%G ru
%F MZM_1968_3_5_a6
We consider a single-line service system with a Palm arrival rate and exponential service time, with $n-1$ places in the queue. Let $\tau_n$ be the moment of first loss of a customer. It is assumed that $\alpha_0=\int_0^\infty e^{-t}dF(t)\to0$ , where $F(t)$ is the distribution function of the time interval between successive arrivals of customers. We shall study the class of limiting distributions of the quantity $\tau_n\delta(\alpha_0)$, where $\delta(\alpha_0)$ is some normalizing factor. We shall obtain conditions for which $P\{\tau_n/M\tau_n.
