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Issue RAIRO Oper. Res.
Volume 38, Number 2, April-June 2004
Advances in modelling of complex systems
Page(s) 121 - 151
DOI 10.1051/ro:2004016

RAIRO Oper. Res. 38 (2004) 121-151
DOI: 10.1051/ro:2004016

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

Jesus R. Artalejo1 and Antonis Economou2

1  Department of Statistics and O.R., Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain; jesus_artalejo@mat.ucm.es.
2  Department of Mathematics, University of Athens Panepistemiopolis, Athens 15784, Greece; aeconom@math.uoa.gr.

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.


Key words: Queueing, Markov decision processes, negative customers, stationary distribution, stochastic comparison.


© EDP Sciences 2004


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