Volume 38, Number 2, April-June 2004Advances in modelling of complex systems
|Page(s)||121 - 151|
|Published online||15 April 2004|
Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers
Department of Statistics and O.R., Faculty of Mathematics,
Complutense University of Madrid, Madrid 28040, Spain;
2 Department of Mathematics, University of Athens Panepistemiopolis, Athens 15784, Greece; email@example.com.
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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