Optimal control and performance analysis of an M X /M/1 queue with batches of negative customers
RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 2, pp. 121-151.

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.

DOI : 10.1051/ro:2004016
Mots-clés : queueing, Markov decision processes, negative customers, stationary distribution, stochastic comparison 
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     author = {Artalejo, Jesus R. and Economou, Antonis},
     title = {Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {121--151},
     publisher = {EDP-Sciences},
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Artalejo, Jesus R.; Economou, Antonis. Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers. RAIRO - Operations Research - Recherche Opérationnelle, Tome 38 (2004) no. 2, pp. 121-151. doi : 10.1051/ro:2004016. http://www.numdam.org/articles/10.1051/ro:2004016/

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