# Entropy maximization and the busy period of some single-server vacation models

Jesus R. Artalejo; Maria J. Lopez-Herrero

RAIRO - Operations Research - Recherche Opérationnelle (2004)

- Volume: 38, Issue: 3, page 195-213
- ISSN: 0399-0559

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topArtalejo, Jesus R., and Lopez-Herrero, Maria J.. "Entropy maximization and the busy period of some single-server vacation models." RAIRO - Operations Research - Recherche Opérationnelle 38.3 (2004): 195-213. <http://eudml.org/doc/245246>.

@article{Artalejo2004,

abstract = {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).},

author = {Artalejo, Jesus R., Lopez-Herrero, Maria J.},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {busy period analysis; maximum entropy methodology; $M/G/1$ vacation models; numerical inversion; Busy period analysis; vacation models},

language = {eng},

number = {3},

pages = {195-213},

publisher = {EDP-Sciences},

title = {Entropy maximization and the busy period of some single-server vacation models},

url = {http://eudml.org/doc/245246},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Artalejo, Jesus R.

AU - Lopez-Herrero, Maria J.

TI - Entropy maximization and the busy period of some single-server vacation models

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 3

SP - 195

EP - 213

AB - 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).

LA - eng

KW - busy period analysis; maximum entropy methodology; $M/G/1$ vacation models; numerical inversion; Busy period analysis; vacation models

UR - http://eudml.org/doc/245246

ER -

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