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

Jesus R. Artalejo; Antonis Economou

RAIRO - Operations Research - Recherche Opérationnelle (2004)

  • Volume: 38, Issue: 2, page 121-151
  • ISSN: 0399-0559

Abstract

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We consider a Markov decision process for an M X / 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.

How to cite

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Artalejo, Jesus R., and Economou, Antonis. "Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers." RAIRO - Operations Research - Recherche Opérationnelle 38.2 (2004): 121-151. <http://eudml.org/doc/245293>.

@article{Artalejo2004,
abstract = {We consider a Markov decision process for an $M^\{X\}/M/1$ 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.},
author = {Artalejo, Jesus R., Economou, Antonis},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {queueing; Markov decision processes; negative customers; stationary distribution; stochastic comparison; Markov decision processesl},
language = {eng},
number = {2},
pages = {121-151},
publisher = {EDP-Sciences},
title = {Optimal control and performance analysis of an $M^\{X\}/M/1$ queue with batches of negative customers},
url = {http://eudml.org/doc/245293},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Artalejo, Jesus R.
AU - Economou, Antonis
TI - Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 2
SP - 121
EP - 151
AB - We consider a Markov decision process for an $M^{X}/M/1$ 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.
LA - eng
KW - queueing; Markov decision processes; negative customers; stationary distribution; stochastic comparison; Markov decision processesl
UR - http://eudml.org/doc/245293
ER -

References

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