服务台可修的离散时间GI/G/1重试排队系统  

Discrete Time GI/G/1 Retrial Queues with Server Breakdowns and Repairs

作　　者：王楠[1] 王金亭[1] 唐晓瑾[2] 

机构地区：[1]北京交通大学理学院,北京100044 [2]北京大学数学科学学院科学与工程计算系,北京100871

出　　处：《武汉理工大学学报（交通科学与工程版）》2008年第4期653-656,共4页Journal of Wuhan University of Technology（Transportation Science & Engineering）

基　　金：国家自然科学基金项目(批准号:10526004;60504016);北京交通大学校基金项目(批准号:2005SM064)资助

摘　　要：讨论了服务器可修的离散时间GI/G/1重试排队系统,其中重试时间服从Bernoulli分布,服务器的寿命为几何分布而修理时间为一般分布.将该系统转化为一个水平相依的拟生灭过程(QBD)并通过矩阵分析方法(MAM)进行分析.通过算法进行逼近,将一个水平相依的Markov链转化为一个有较大边界的与水平不相依的Markov链.最终得到了重试空间中顾客人数的分布,并且通过一些数值算例进一步说明了不同参数对系统的影响.A discrete time GI/G/1 retrial queue is studied, where the retrial time has a geometrical distribution and the server is subject to breakdowns and repairs. It is assumed that the server has a geometrical lifetime and the repair time has a general distribution. The discrete GI/G/1 retrial system can be analyzed as a level dependent QBD process and the resulting QBD can be analyzed by the Matrix analytic method （MAM） conveniently. The algorithmic approach to this model is exploited and the level dependent Markov chain is approximated with a level independent Markov chain that has a large set of boundaries. The distribution of the number of jobs in the orbit is obtained, and finally, some numerical examples show the influence of the parameters on several performance characteristics.

关 键 词：重试排队 可修排队 矩阵分析方法 拟生灭过程 

分 类 号：O226[理学—运筹学与控制论]