Document 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 Economou21 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