In this paper, we analyse a discrete-time queue with a primary server of high service capacity and a substitute server of low service capacity. Disasters that only arrive during the busy periods of the primary server remove all customers from the system and make the primary server breakdown. When the primary server fails and is being repaired, the substitute server handles arriving customers. Applying the embedded Markov chain technique and the supplementary variable method, we determine the distribution of the system length at departure epochs and the joint distribution of the queue length and server’s state at an arbitrary instant. Then we derive the sojourn time distribution. We also provide the probability generating function of the time between failures. Some numerical examples are delivered to give an insight into the impact of system parameters on performance measures and a cost function.
Accepté le :
DOI : 10.1051/ro/2018057
Mots-clés : Discrete-time queue, disasters, working breakdowns, performance analysis
@article{RO_2019__53_4_1197_0,
author = {Gao, Shan and Wang, Jinting and Van Do, Tien},
title = {Analysis of a discrete-time repairable queue with disasters and working breakdowns},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1197--1216},
publisher = {EDP-Sciences},
volume = {53},
number = {4},
year = {2019},
doi = {10.1051/ro/2018057},
mrnumber = {3986369},
zbl = {1439.60085},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2018057/}
}
TY - JOUR AU - Gao, Shan AU - Wang, Jinting AU - Van Do, Tien TI - Analysis of a discrete-time repairable queue with disasters and working breakdowns JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1197 EP - 1216 VL - 53 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018057/ DO - 10.1051/ro/2018057 LA - en ID - RO_2019__53_4_1197_0 ER -
%0 Journal Article %A Gao, Shan %A Wang, Jinting %A Van Do, Tien %T Analysis of a discrete-time repairable queue with disasters and working breakdowns %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1197-1216 %V 53 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018057/ %R 10.1051/ro/2018057 %G en %F RO_2019__53_4_1197_0
Gao, Shan; Wang, Jinting; Van Do, Tien. Analysis of a discrete-time repairable queue with disasters and working breakdowns. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1197-1216. doi : 10.1051/ro/2018057. http://www.numdam.org/articles/10.1051/ro/2018057/
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