An M/G/1 retrial queue with single working vacation under Bernoulli schedule

Li, Tao; Zhang, Liyuan; Gao, Shan

doi:10.1051/ro/2019008

Li, Tao ; Zhang, Liyuan ; Gao, Shan

RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 471-488.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q, he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.

MR Zbl

DOI : 10.1051/ro/2019008

Classification : 60k25, 90B22
Mots-clés : Retrial, working vacation, Bernoulli, embedded Markov chain, supplementary variable method

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     author = {Li, Tao and Zhang, Liyuan and Gao, Shan},
     title = {An {M/G/1} retrial queue with single working vacation under {Bernoulli} schedule},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {471--488},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {2},
     year = {2020},
     doi = {10.1051/ro/2019008},
     mrnumber = {4070784},
     zbl = {1434.60264},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019008/}
}

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Li, Tao; Zhang, Liyuan; Gao, Shan. An M/G/1 retrial queue with single working vacation under Bernoulli schedule. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 471-488. doi : 10.1051/ro/2019008. http://www.numdam.org/articles/10.1051/ro/2019008/

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