Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations
This paper analyzes a finite buffer size discrete-time Geo/G/1/N queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/160697 |
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| _version_ | 1832568095342854144 |
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| author | Chuanyi Luo Jiangyi Li Yinghui Tang |
| author_facet | Chuanyi Luo Jiangyi Li Yinghui Tang |
| author_sort | Chuanyi Luo |
| collection | DOAJ |
| description | This paper analyzes a finite buffer size discrete-time Geo/G/1/N queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method. |
| format | Article |
| id | doaj-art-a63235c26e8e47e4b39ee72dbcfc44fb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a63235c26e8e47e4b39ee72dbcfc44fb2025-02-03T00:59:49ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/160697160697Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working VacationsChuanyi Luo0Jiangyi Li1Yinghui Tang2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaResearch Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu 611130, ChinaSchool of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaThis paper analyzes a finite buffer size discrete-time Geo/G/1/N queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method.http://dx.doi.org/10.1155/2015/160697 |
| spellingShingle | Chuanyi Luo Jiangyi Li Yinghui Tang Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations Discrete Dynamics in Nature and Society |
| title | Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations |
| title_full | Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations |
| title_fullStr | Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations |
| title_full_unstemmed | Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations |
| title_short | Study on the Queue-Length Distribution in Geo/G(MWV)/1/N Queue with Working Vacations |
| title_sort | study on the queue length distribution in geo g mwv 1 n queue with working vacations |
| url | http://dx.doi.org/10.1155/2015/160697 |
| work_keys_str_mv | AT chuanyiluo studyonthequeuelengthdistributioningeogmwv1nqueuewithworkingvacations AT jiangyili studyonthequeuelengthdistributioningeogmwv1nqueuewithworkingvacations AT yinghuitang studyonthequeuelengthdistributioningeogmwv1nqueuewithworkingvacations |