On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations
We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined thre...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/587163 |
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| _version_ | 1832554267614904320 |
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| author | Sung J. Kim Nam K. Kim Hyun-Min Park Kyung Chul Chae Dae-Eun Lim |
| author_facet | Sung J. Kim Nam K. Kim Hyun-Min Park Kyung Chul Chae Dae-Eun Lim |
| author_sort | Sung J. Kim |
| collection | DOAJ |
| description | We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases. |
| format | Article |
| id | doaj-art-0aedebd48eb441729651386cc2238df9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0aedebd48eb441729651386cc2238df92025-02-03T05:51:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/587163587163On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple VacationsSung J. Kim0Nam K. Kim1Hyun-Min Park2Kyung Chul Chae3Dae-Eun Lim4Department of Management Engineering, Sangmyung University, Cheonan 330-720, Republic of KoreaDepartment of Industrial Engineering, Chonnam National University, Gwangju 500-757, Republic of KoreaDepartment of Business Administration, Pai Chai University, Daejeon 302-735, Republic of KoreaDepartment of Industrial and Systems Engineering, KAIST, Daejon 305-701, Republic of KoreaDivision of Business and Commerce, Baekseok University, Cheonan 330-704, Republic of KoreaWe consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases.http://dx.doi.org/10.1155/2013/587163 |
| spellingShingle | Sung J. Kim Nam K. Kim Hyun-Min Park Kyung Chul Chae Dae-Eun Lim On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations Journal of Applied Mathematics |
| title | On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations |
| title_full | On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations |
| title_fullStr | On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations |
| title_full_unstemmed | On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations |
| title_short | On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations |
| title_sort | on the discrete time geox g 1 queues under n policy with single and multiple vacations |
| url | http://dx.doi.org/10.1155/2013/587163 |
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