| TRANSIENT SOLUTION FOR QUEUE-LENGTH DISTRIBUTION OF Geometry/G/1 QUEUEING MODEL |
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| 作者姓名： | Luo Chuanyi Tang Yinghui Liu Renbin |
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| 作者单位： | [1]Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China [2]Department of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066,China. [3]School of Mathematics and Physics, Chongqing Institute of Technology, Chongqing 400050,China. |
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| 基金项目： | 西南财经大学校科研和教改项目
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四川师范大学校科研和教改项目 |
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| 摘 要： | In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.
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| 关 键 词： | 队列长度分布 瞬时解 概率分解技术 离散时间几何/G/1队列模型 |
| 收稿时间： | 2005-11-11 |
Transient solution for queue-length distribution of Geometry/<Emphasis Type="Italic">G</Emphasis>/1 queueing model |
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| Luo Chuanyi Tang Yinghui Liu Renbin.TRANSIENT SOLUTION FOR QUEUE-LENGTH DISTRIBUTION OF Geometry/G/1 QUEUEING MODEL[J].Applied Mathematics A Journal of Chinese Universities,2007,22(1):95-100. |
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| Authors: | Luo Chuanyi Tang Yinghui Liu Renbin |
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| Institution: | (1) Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China;(2) Department of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China;(3) School of Mathematics and Physics, Chongqing Institute of Technology, Chongqing, 400050, China |
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| Abstract: | In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric(parameter p) distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj}, j ≥ 1 is studied. By a simple method (techniques of probability decomposition, renewal process theory) that is different from the techniques used by Hunter(1983), the transient property of the queue with initial state i(i ≥ 0) is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n is obtained, and the recursion expression of the limiting queue length distribution is also obtained. |
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| Keywords: | discrete time queue u-transform transient distribution stationary distribution recursion expression |
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