The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations
This paper deals with a discrete-time bulk-service Geo/Geo/1 queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a ran...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/587269 |
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| _version_ | 1832545481666854912 |
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| author | Jiang Cheng Yinghui Tang Miaomiao Yu |
| author_facet | Jiang Cheng Yinghui Tang Miaomiao Yu |
| author_sort | Jiang Cheng |
| collection | DOAJ |
| description | This paper deals with a discrete-time bulk-service Geo/Geo/1
queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time n. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results. |
| format | Article |
| id | doaj-art-f5e49d1cc443454ca2d86b784c0ef35c |
| 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-f5e49d1cc443454ca2d86b784c0ef35c2025-02-03T07:25:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/587269587269The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working VacationsJiang Cheng0Yinghui Tang1Miaomiao Yu2School of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaSchool of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaSchool of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaThis paper deals with a discrete-time bulk-service Geo/Geo/1 queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time n. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results.http://dx.doi.org/10.1155/2013/587269 |
| spellingShingle | Jiang Cheng Yinghui Tang Miaomiao Yu The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations Journal of Applied Mathematics |
| title | The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations |
| title_full | The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations |
| title_fullStr | The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations |
| title_full_unstemmed | The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations |
| title_short | The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations |
| title_sort | discrete time bulk service geo geo 1 queue with multiple working vacations |
| url | http://dx.doi.org/10.1155/2013/587269 |
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