The $M/M/1$ queue is considered in the case in which customers are
served in random order. A formula is obtained for the distribution of the
waiting time w in the stationary state. The formula is used to show that
$P9w > t) \sim \alpha t^{-5/6} \exp (-\beta t - \gamma t^{1/3})$ as $t \to
\infty$, with the constants $\alpha, \beta$, and $\gamma$ expressed as
functions of the traffic intensity $\rho$. The distribution of w for the
random order discipline is compared to that of the first in, first out
discipline.
Publié le : 1997-05-14
Classification:
$M/M/1$ queue,
random order service discipline,
waiting time distribution,
Little's law,
60K25,
90B22,
30C20,
30D20,
44R10
@article{1034625337,
author = {Flatto, L.},
title = {The waiting time distribution for the random order service $M/M/1$
queue},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 382-409},
language = {en},
url = {http://dml.mathdoc.fr/item/1034625337}
}
Flatto, L. The waiting time distribution for the random order service $M/M/1$
queue. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 382-409. http://gdmltest.u-ga.fr/item/1034625337/