| AN M/G/1 RETRIAL QUEUE WITH SECOND MULTI-OPTIONAL SERVICE, FEEDBACK AND UNRELIABLE SERVER |
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| 引用本文： | Li Jianghua Wang Jinting. AN M/G/1 RETRIAL QUEUE WITH SECOND MULTI-OPTIONAL SERVICE, FEEDBACK AND UNRELIABLE SERVER[J]. 高校应用数学学报(英文版), 2006, 21(3): 252-262. DOI: 10.1007/s11766-003-0002-9 |
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| 作者姓名： | Li Jianghua Wang Jinting |
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| 作者单位： | Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China. |
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| 基金项目： | BJTU Research Foundation （2005SM064）, the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, Education Ministry and the National Natural Science Foundation of China （10526004, 60504016）. |
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| 摘 要： | An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.
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| 关 键 词： | 复审队列 两相服务 反馈 服务器修理 启动失败 |
| 收稿时间： | 2005-09-09 |
| 修稿时间： | 2006-02-20 |
An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server |
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| Li Jianghua,Wang Jinting. An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(3): 252-262. DOI: 10.1007/s11766-003-0002-9 |
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| Authors: | Li Jianghua Wang Jinting |
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| Affiliation: | (1) Department of Mathematics, Beijing Jiaotong University, 100044 Beijing, China |
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| Abstract: | An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained. Research sponsored by BJTU Research Foundation (2005SM064), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Education Ministry and the National Natural Science Foundation of China (10526004, 60505016) |
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| Keywords: | retrial queues two-phase service feedback server breakdown and repair starting failures. |
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