頁籤選單縮合
題 名 | Censoring Technique Applied to a Map/G/1 Queue with Set-up Time and Multiple Vacations |
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作 者 | 張振中; 童金英; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 15:2 2011.04[民100.04] |
頁 次 | 頁607-622 |
分類號 | 319.9 |
關鍵詞 | Markovian arrival process; MAP; Multiple vacations; Censoring technique; RG-factorization; Matrix-analytic method; |
語 文 | 英文(English) |
英文摘要 | Infinite state Markov chains with block-structured transition matrix find extensive applications in many areas, including telecommunications, and queueing systems, for example. In this paper, we use the censoring technique to study a MAP/G/1 queue with set-up time and multiple vacations, whose transition matrix can be transformed to a block-Toeplitz or block-repeating structured. Hence, we are able to relate the boundary conditions of the system to a Markov chain of M/G/1 type. This leads to a solution of the boundary equations, which is crucial for solving the system of differential equations. We also provide expressions for the distribution of stationary queue length, virtual waiting time and the busy period, respectively. |
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