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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Hindawi Limited
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/241636 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |