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.

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 i with probability q i , i = 1 , 2 , ... , d . 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.

DOI : 10.1051/ro/2018021
Classification : 68M20, 60K20, 90B22
Mots-clés : Server breakdown, geometric abandonments, sojourn time, cycle analysis
Jiang, Tao 1 ; Xin, Baogui 1 ; Chang, Baoxian 1 ; Liu, Liwei 1

1 
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     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},
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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://archive.numdam.org/articles/10.1051/ro/2018021/

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