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| 具有可变到达率的多重休假Geo~(λ_1,λ_2)/G/1排队分析 | |
| 引用本文： | 骆川义,唐应辉.具有可变到达率的多重休假Geo~(λ_1,λ_2)/G/1排队分析[J].数学学报,2010,53(4):805-816. |
| 作者姓名： | 骆川义 唐应辉 |
| 作者单位： | 1. 西南财经大学经济数学学院 成都 611130; 2. 四川师范大学数学与软件科学学院 成都 610066 |
| 基金项目： | 国家自然科学基金资助项目(70871084);教育部高校博士点专项基金项目(200806360001);西南财经大学科学研究基金及西南财经大学211工程三期建设青年教师成长项目 |
| 摘 要： | 本文考虑顾客到达与服务员休假相关的多重休假离散时间排队系统,用更新过程及u-变换分析了系统的队长性质.分别得到系统在三种时点(n~-,n~+,n)处的队长分布的递推解,进而揭示了在不同到达率条件下系统队长分布不再具有随机分解特性,得到了系统在四种时点(n~-,n~+,n,离去时点D_n)处稳态队长分布的重要关系(不同于连续时间排队系统). |
| 关 键 词： | 离散时间排队 多重休假 递推解 可变到达率 |
| 收稿时间： | 2009-08-25 |
| 修稿时间： | 2010-03-16 |
Analysis of a Multi-Vacation Geoλ1,λ2/G/1 Queue with Variable Arrival Rate |
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| Institution: | 1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China; 2. School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China |
| Abstract: | In this paper, we consider a discrete time multi-vacation queueing system with variable arrival rate. Using renewal process and u-transform, we study the queue size properties and derive the recursive expressions of the queue size distribution at any epoch n-,n+ and n The results obtained in this paper indicate that the equilibrium queue size distribution no longer follows the stochastic decomposition discipline. Furthermore the important relations between equilibrium queue size distributions at different epochs (n-,n+,n and departure epoch Dn). are discovered (being different from the corresponding relations given in continuous queueing system). |
| Keywords: | discrete time queue multi-vacation recursive expression variable arrival rate |
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