Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations |
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Authors: | Yuanyuan Liu Yiqiang Q Zhao |
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Institution: | 1. School of Mathematics and Statistics, Railway Campus, Central South University, Changsha, Hunan 410075, China;2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 |
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Abstract: | In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N-(V, E)-queue. Exact asymptotic rates of the loss probability are obtained for the cases in which the traffic intensity is smaller than, equal to and greater than one, respectively. When the vacation time is zero, the model considered degenerates to the standard M/G/1/N queue. For this standard queueing model, our analysis provides new or extended asymptotic results for the loss probability. In terms of the duality relationship between the M/G/1/N and GI/M/1/N queues, we also provide asymptotic properties for the standard GI/M/1/N model. |
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Keywords: | M/G/1/N queue GI/M/1/N queue Serve vacations Invariant measure Loss probability Asymptotic behavior |
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