RAIRO - Operations Research

Research Article

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

Artalejo, Jesus R.a1 and Economou, Antonisa2

a1 Department of Statistics and O.R., Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain; jesus_artalejo@mat.ucm.es.

a2 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.

(Online publication April 15 2004)

Key Words:

  • Queueing;
  • Markov decision processes;
  • negative customers;
  • stationary distribution;
  • stochastic comparison.
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