Cost optimization of queueing systems with interruptions
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 371-382
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We consider a queueing system $M|G|1$ with possible vacations in server
operations for principal customers (for example, if a server is leased).
A cost optimization problem is solved. As control parameters, we use the
probability $\alpha$ of the vacation and its duration. Under fairly general
assumptions about the system behavior during vacations, we show that the
optimal value of the probability $\alpha$ is either 0 or 1. We also give
necessary and sufficient conditions for a vacation to be carried out, i.e.,
$\alpha=1$. With constant vacation durations, we find conditions such that
$\alpha=1$, and the vacation duration is optimal. Two examples are
considered. In the first example, the revenue from the vacation is a linear
function of its duration, and, in the second example, the revenue is
a quadratic function.
Keywords:
queueing system, queueing vacation, stationary distribution.
@article{TVP_2023_68_2_a8,
author = {G. A. Afanasiev},
title = {Cost optimization of queueing systems with interruptions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {371--382},
publisher = {mathdoc},
volume = {68},
number = {2},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a8/}
}
G. A. Afanasiev. Cost optimization of queueing systems with interruptions. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 371-382. http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a8/