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

Jesus R. Artalejo; Maria J. Lopez-Herrero

RAIRO - Operations Research (2010)

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

Abstract

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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).

How to cite

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Artalejo, Jesus R., and Lopez-Herrero, Maria J.. "Entropy maximization and the busy period of some single-server vacation models." RAIRO - Operations Research 38.3 (2010): 195-213. <http://eudml.org/doc/105310>.

@article{Artalejo2010,
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},
keywords = {Busy period analysis; maximum entropy methodology; M/G/1 vacation models; numerical inversion.; vacation models; numerical inversion},
language = {eng},
month = {3},
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/105310},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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.; vacation models; numerical inversion
UR - http://eudml.org/doc/105310
ER -

References

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