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Optimal control and performance analysis of an MX/M/1 queue withbatchesof negative customers

Published online by Cambridge University Press:  15 April 2004

Jesus R. Artalejo  and
Antonis Economou
Jesus R. Artalejo
Affiliation:
Department of Statistics and O.R., Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain; jesus_artalejo@mat.ucm.es.
Antonis Economou
Affiliation:
Department of Mathematics, University of Athens Panepistemiopolis, Athens 15784, Greece; aeconom@math.uoa.gr.
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Abstract

We consider a Markov decision process for an MX/M/1 queue that iscontrolled by batches of negative customers. More specifically, we deriveconditions that imply threshold-type optimal policies, under either thetotal discounted cost criterion or the average cost criterion. Theperformance analysis of the model when it operates under a giventhreshold-type policy is also studied. We prove a stability condition and acomplete stochastic comparison characterization for models operating underdifferent thresholds. Exact and asymptotic results concerning thecomputation of the stationary distribution of the model are also derived.

Keywords

QueueingMarkov decision processesnegative customersstationary distributionstochastic comparison.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 2: Advances in modelling of complex systems , April 2004 , pp. 121 - 151
Copyright
© EDP Sciences, 2004

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