Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers
•We introduce orbital search and impatient customers into a repairable M/G/1-G retrial queue.•We present the stationary condition of the system and steady-state analysis.•We present the analysis of the distribution of the waiting time.•Some main reliability measures are provided. This paper treats a...
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| Published in | European journal of operational research Vol. 236; no. 2; pp. 561 - 572 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
16.07.2014
Elsevier Sequoia S.A |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-2217 1872-6860 |
| DOI | 10.1016/j.ejor.2014.01.065 |
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| Abstract | •We introduce orbital search and impatient customers into a repairable M/G/1-G retrial queue.•We present the stationary condition of the system and steady-state analysis.•We present the analysis of the distribution of the waiting time.•Some main reliability measures are provided.
This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented. |
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| AbstractList | This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented. [PUBLICATION ABSTRACT] This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented. •We introduce orbital search and impatient customers into a repairable M/G/1-G retrial queue.•We present the stationary condition of the system and steady-state analysis.•We present the analysis of the distribution of the waiting time.•Some main reliability measures are provided. This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using embedded Markov chain technique and the supplementary variable method, we present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state. The waiting process is also given. Some main reliability measures, such as the availability, failure frequency, and the reliability function of the server, are obtained. Finally, some numerical examples and cost optimization analysis are presented. |
| Author | Gao, Shan Wang, Jinting |
| Author_xml | – sequence: 1 givenname: Shan surname: Gao fullname: Gao, Shan email: sgao_09@Yeah.net organization: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China – sequence: 2 givenname: Jinting surname: Wang fullname: Wang, Jinting email: jtwang@bjtu.edu.cn organization: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China |
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Information Systems and Operational Research doi: 10.1080/03155986.2000.11732399 – volume: 63 start-page: 776 year: 2006 ident: 10.1016/j.ejor.2014.01.065_b0060 article-title: Analysis of a multi-server retrial queue with search of customers from the orbit publication-title: Performance Evaluation doi: 10.1016/j.peva.2005.09.002 – volume: 16 start-page: 464 issue: 5 year: 2006 ident: 10.1016/j.ejor.2014.01.065_b0110 article-title: Reliability analysis of M/G/1 queues with general retrial times and server breakdowns publication-title: Progress in Natural Science doi: 10.1080/10020070612330021 – year: 2008 ident: 10.1016/j.ejor.2014.01.065_b0030 – volume: 5 start-page: 179 issue: 2 year: 2008 ident: 10.1016/j.ejor.2014.01.065_b0125 article-title: A repairable M/G/1 retrial queue with Bernoulli vacation and two-phase service publication-title: Quality Technology and Quantitative Management doi: 10.1080/16843703.2008.11673395 – volume: 1 start-page: 30 year: 2005 ident: 10.1016/j.ejor.2014.01.065_b0135 article-title: An M/G/1 retrial queue with balking and retrials during service publication-title: International Journal of Operational Research doi: 10.1504/IJOR.2005.007432 – volume: 126 start-page: 233 issue: 2 year: 2000 ident: 10.1016/j.ejor.2014.01.065_b0015 article-title: G-networks: A versatile approach for work removal in queueing networks publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(99)00476-2 |
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| Snippet | •We introduce orbital search and impatient customers into a repairable M/G/1-G retrial queue.•We present the stationary condition of the system and... This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals. After a completion... |
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| StartPage | 561 |
| SubjectTerms | Cost analysis Customers Distribution Failure Markov analysis Mathematical models Negative customers Orbital search Orbitals Queueing Queues Queuing theory Reliability Searching Servers Studies |
| Title | Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers |
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