On the discrete-time system with server breakdowns: Computational algorithm and optimization algorithm
This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break dow...
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| Published in | Applied mathematics and computation Vol. 218; no. 7; pp. 3624 - 3634 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.12.2011
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| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2011.09.003 |
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| Abstract | This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break down even if the system is idle. The server lifetimes are assumed to be geometrical and the server repair times are also geometric distributions. We model this system by the level-dependent quasi-birth–death (QBD) process and develop computation algorithms of the stationary distribution of the number of customers in the system using the matrix analytic method. The search algorithm for parameter optimization based on a cost model is developed and performed herein. |
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| AbstractList | This paper analyzes a discrete-time Geo/Geo/1 queueing system with the server subject to breakdowns and repairs, in which two different possible types of the server breakdowns are considered. In Type 1, the server may break down only when the system is busy, while in Type 2, the server can break down even if the system is idle. The server lifetimes are assumed to be geometrical and the server repair times are also geometric distributions. We model this system by the level-dependent quasi-birth–death (QBD) process and develop computation algorithms of the stationary distribution of the number of customers in the system using the matrix analytic method. The search algorithm for parameter optimization based on a cost model is developed and performed herein. |
| Author | Ke, Jau-Chuan Lin, Chuen-Horng |
| Author_xml | – sequence: 1 givenname: Chuen-Horng surname: Lin fullname: Lin, Chuen-Horng email: linch@ntit.edu.tw organization: Department of Computer Science and Information Engineering, National Taichung Institute of Technology, Taichung 404, Taiwan, ROC – sequence: 2 givenname: Jau-Chuan surname: Ke fullname: Ke, Jau-Chuan email: jauchuan@ntit.edu.tw organization: Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, ROC |
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| Cites_doi | 10.1111/j.2517-6161.1962.tb00438.x 10.1142/S0217595906000929 10.1137/1.9780898719734 10.3844/ajassp.2008.565.573 10.1080/16843703.2004.11673079 10.2307/3215393 10.1016/j.cie.2006.04.004 10.1111/1475-3995.00350 10.1016/j.cie.2003.11.001 10.1287/opre.6.1.96 10.1016/S0026-2714(96)00018-2 10.1016/S0360-8352(02)00235-8 10.1108/02644400810909616 10.1016/j.camwa.2004.06.024 10.1016/j.cie.2008.07.010 |
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| SubjectTerms | Algorithms Breakdown Breakdowns Breaking down Computation Discrete time queue Mathematical models Matrix analytic approach Optimization Quasi-birth–death Quasi-Newton method Repairing Servers |
| Title | On the discrete-time system with server breakdowns: Computational algorithm and optimization algorithm |
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