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

Published online by Cambridge University Press:  15 April 2004

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 is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived.

Type
Research Article
Copyright
© EDP Sciences, 2004

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