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

Published online by Cambridge University Press:  15 September 2004

Jesus R. Artalejo  and
Maria J. Lopez-Herrero
Jesus R. Artalejo
Affiliation:
Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain; [email protected].
Maria J. Lopez-Herrero
Affiliation:
School of Statistics, Complutense University of Madrid, Madrid 28040, Spain; [email protected].
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Abstract

In this paper, information theoretic methodology forsystem modeling is applied to investigate the probability density functionof the busy period in M/G/1 vacation models operating under the N-, T- andD-policies. The information about the density function is limited to a fewmean value constraints (usually the first moments). By using the maximumentropy methodology one obtains the least biased probability densityfunction satisfying the system's constraints. The analysis of the threecontrollable M/G/1 queueing models provides a parallel numerical study ofthe 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, inmost cases, reduces to discrete queueing measures (such as the number ofcustomers in the system).

Keywords

Busy period analysismaximum entropy methodologyM/G/1vacation modelsnumerical inversion.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 3 , July 2004 , pp. 195 - 213
Copyright
© EDP Sciences, 2004

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