Entropy maximization and the busy period of some single-server vacation models
RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 195-213.

In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in $M/G/1$ vacation models operating under the $N$-, $T$- and $D$-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system’s constraints. The analysis of the three controllable $M/G/1$ queueing models provides a parallel numerical study of the solution obtained via the maximum entropy approach versus “classical” solutions. The maximum entropy analysis of a continuous system descriptor (like the busy period) enriches the current body of literature which, in most cases, reduces to discrete queueing measures (such as the number of customers in the system).

DOI : https://doi.org/10.1051/ro:2004020
Mots clés : busy period analysis, maximum entropy methodology, $M/G/1$ vacation models, numerical inversion
@article{RO_2004__38_3_195_0,
author = {Artalejo, Jesus R. and Lopez-Herrero, Maria J.},
title = {Entropy maximization and the busy period of some single-server vacation models},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {195--213},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
doi = {10.1051/ro:2004020},
zbl = {pre02110162},
mrnumber = {2091752},
language = {en},
url = {www.numdam.org/item/RO_2004__38_3_195_0/}
}
Artalejo, Jesus R.; Lopez-Herrero, Maria J. Entropy maximization and the busy period of some single-server vacation models. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 3, pp. 195-213. doi : 10.1051/ro:2004020. http://www.numdam.org/item/RO_2004__38_3_195_0/

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