The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time

Ye, Qingqing; Liu, Liwei; Jiang, Tao; Chang, Baoxian

doi:10.1051/ro/2019020

Ye, Qingqing ; Liu, Liwei ; Jiang, Tao ; Chang, Baoxian

RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 3, pp. 675-691.

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, we study the discrete-time MAP/PH/1 queue with multiple working vacations and finite buffer N. Using the Matrix-Geometric Combination method, we obtain the stationary probability vectors of this model, which can be expressed as a linear combination of two matrix-geometric vectors. Furthermore, we obtain some performance measures including the loss probability and give the limit of loss probability as finite buffer N goes to infinite. Waiting time distribution is derived by using the absorbing Markov chain. Moreover, we obtain the number of customers served in the busy period. At last, some numerical examples are presented to verify the results we obtained and show the impact of parameter N on performance measures.

MR Zbl

DOI : 10.1051/ro/2019020

Classification : 60K25, 68M20
Mots-clés : Working vacation, finite buffer, matrix-geometric combination method, Sojourn time, busy period

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     title = {The analysis of a discrete time finite-buffer queue with working vacations under {Markovian} arrival process and {PH-service} time},
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     pages = {675--691},
     publisher = {EDP-Sciences},
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Ye, Qingqing; Liu, Liwei; Jiang, Tao; Chang, Baoxian. The analysis of a discrete time finite-buffer queue with working vacations under Markovian arrival process and PH-service time. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 3, pp. 675-691. doi : 10.1051/ro/2019020. http://archive.numdam.org/articles/10.1051/ro/2019020/

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