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N-控制策略且温储备失效M/G/1可修排队

ISSN号：1000-5781
期刊名称：系统工程学报
时间：2015.12.1
页码：852-864
分类：O226[理学—运筹学与控制论;理学—数学] TN915.2[电子电信—通信与信息系统;电子电信—信息与通信工程]
作者机构：[1]School of Physics and Mechanical and Electrical Engineering , Hexi University, Zhangye 734000, China., [2]School of Mathematics and Statistics, Hexi University, Zhangyc 734000, China., [3]School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China., [4]School of Science, Sichuan University of Science and Engineering, Zigong 643000, China.
相关基金：This research was supported by the National Natural Science Foundation of China under Grant Nos. 71171138, 71301111, 71571127, and the Scientific Research Innovation ＆ Application Foundation of Headmaster of Hexi University under Grant Nos. XZ2013-06, XZ2013-09.
相关项目：基于排队分析技术的随机环境下供应链库存理论及应用研究

关键词：队列长度, 大小分布, 地理, 稳态队长, 长度分布, 离散时间, 递推公式, 数值结果, Min（N,D）-policy discrete-time queue, queue length distribution, system capacity opti mum design, total probability decomposition technique, z-transform.

中文摘要：

这份报纸在 Min 下面考虑一个分离时间的 Geo/G/1 队列( N ， D )闲散服务器在恢复它的服务的政策如果任何一个 N 顾客在系统或总数积累，服务的积压事物等待的顾客预定超过 D ，无论哪个首先发生( Min ( N ， D )-policy)。由使用更新过程理论和全部的概率分解技术，作者学习短暂并且从任意的起始的状态的开始的队列长度的平衡性质，并且两个都为在任意的时间时代 n ⁺计算稳定的州的队列长度获得短暂队列长度分发和递归的公式的z转变的递归的表示。同时，作者获得另外的队列长度分发的明确的表情。而且，在在不同时间时代 n ^-, n 和 n ⁺ 的稳定的州的队列长度分布之间的重要关系是也报导了。最后，作者给数字例子在稳定的州的队列长度分发上说明系统参数的效果，并且也从数字结果证明长度分发在系统能力设计是重要的稳定的状态的表达式排队。

英文摘要：

This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l~trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.

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