This paper studies a single server queueing model in a multi-phase random environment with server breakdowns and geometric abandonments, where server breakdowns only occur while the server is in operation. At a server breakdown instant (i.e., an abandonment opportunity epoch), all present customers adopt the so-called geometric abandonments, that is, the customers decide sequentially whether they will leave the system or not. In the meantime, the server abandons the service and a repair process starts immediately. After the server is repaired, the server resumes its service, and the system enters into the operative phase with probability . Using probability generating functions and matrix geometric approach, we obtain the steady state distribution and various performance measures. In addition, some numerical examples are presented to show the impact of parameters on the performance measures.
Mots clés : Server breakdown, geometric abandonments, sojourn time, cycle analysis
@article{RO_2018__52_3_903_0,
author = {Jiang, Tao and Xin, Baogui and Chang, Baoxian and Liu, Liwei},
title = {Analysis of a queueing system in random environment with an unreliable server and geometric abandonments},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {903--922},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/ro/2018021},
zbl = {1408.90073},
mrnumber = {3868451},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2018021/}
}
TY - JOUR AU - Jiang, Tao AU - Xin, Baogui AU - Chang, Baoxian AU - Liu, Liwei TI - Analysis of a queueing system in random environment with an unreliable server and geometric abandonments JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 903 EP - 922 VL - 52 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018021/ DO - 10.1051/ro/2018021 LA - en ID - RO_2018__52_3_903_0 ER -
%0 Journal Article %A Jiang, Tao %A Xin, Baogui %A Chang, Baoxian %A Liu, Liwei %T Analysis of a queueing system in random environment with an unreliable server and geometric abandonments %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 903-922 %V 52 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018021/ %R 10.1051/ro/2018021 %G en %F RO_2018__52_3_903_0
Jiang, Tao; Xin, Baogui; Chang, Baoxian; Liu, Liwei. Analysis of a queueing system in random environment with an unreliable server and geometric abandonments. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 903-922. doi : 10.1051/ro/2018021. http://www.numdam.org/articles/10.1051/ro/2018021/
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