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.

@article{RO_2004__38_2_121_0, 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}, volume = {38}, number = {2}, year = {2004}, doi = {10.1051/ro:2004016}, mrnumber = {2081834}, zbl = {1092.90013}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro:2004016/} }

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 SP - 121 EP - 151 VL - 38 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2004016/ DO - 10.1051/ro:2004016 LA - en ID - RO_2004__38_2_121_0 ER -

%0 Journal Article %A Artalejo, Jesus R. %A Economou, Antonis %T Optimal control and performance analysis of an $M^{X}/M/1$ queue with batches of negative customers %J RAIRO - Operations Research - Recherche Opérationnelle %D 2004 %P 121-151 %V 38 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2004016/ %R 10.1051/ro:2004016 %G en %F RO_2004__38_2_121_0

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, Volume 38 (2004) no. 2, pp. 121-151. doi : 10.1051/ro:2004016. http://archive.numdam.org/articles/10.1051/ro:2004016/

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