Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
This paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/241636 |
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| _version_ | 1832566229056880640 |
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| author | Renbin Liu |
| author_facet | Renbin Liu |
| author_sort | Renbin Liu |
| collection | DOAJ |
| description | This paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during (0,t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server Mξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose. |
| format | Article |
| id | doaj-art-ae62f70ec6264c96bd791e7c01a303b5 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ae62f70ec6264c96bd791e7c01a303b52025-02-03T01:04:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/241636241636Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation QueueRenbin Liu0School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaThis paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during (0,t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server Mξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.http://dx.doi.org/10.1155/2014/241636 |
| spellingShingle | Renbin Liu Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue Journal of Applied Mathematics |
| title | Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue |
| title_full | Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue |
| title_fullStr | Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue |
| title_full_unstemmed | Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue |
| title_short | Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue |
| title_sort | probabilistic decomposition method on the serverindices of an mξ g 1 vacation queue |
| url | http://dx.doi.org/10.1155/2014/241636 |
| work_keys_str_mv | AT renbinliu probabilisticdecompositionmethodontheserverindicesofanmxg1vacationqueue |