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

Jesus R. Artalejo; Antonis Economou

RAIRO - Operations Research (2010)

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

Abstract

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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.

How to cite

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Artalejo, Jesus R., and Economou, Antonis. "Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers." RAIRO - Operations Research 38.2 (2010): 121-151. <http://eudml.org/doc/105305>.

@article{Artalejo2010,
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. },
author = {Artalejo, Jesus R., Economou, Antonis},
journal = {RAIRO - Operations Research},
keywords = {Queueing; Markov decision processes; negative customers; stationary distribution; stochastic comparison.; queueing; Markov decision processesl; stationary distribution; stochastic comparison},
language = {eng},
month = {3},
number = {2},
pages = {121-151},
publisher = {EDP Sciences},
title = {Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers},
url = {http://eudml.org/doc/105305},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Artalejo, Jesus R.
AU - Economou, Antonis
TI - Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 2
SP - 121
EP - 151
AB - 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.
LA - eng
KW - Queueing; Markov decision processes; negative customers; stationary distribution; stochastic comparison.; queueing; Markov decision processesl; stationary distribution; stochastic comparison
UR - http://eudml.org/doc/105305
ER -

References

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