服务率可变且窗口能力不等的M/M/n排队模型研究  

On M/M/n Queueing Model with the Different Ability of the Windows and Changeable Service Rate

作　　者：侯冬倩[1] 高世泽[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2010年第2期46-48,共3页Journal of Chongqing Normal University:Natural Science

摘　　要：对于窗口能力不等的多服务窗排队模型,一些研究结果是在各服务窗服务率不变的条件下给出的。为了满足实际生活的需要,本文建立了窗口能力不等且服务率可变的M/M/n排队模型,模型假定顾客的到达时间间隔服从参数为λ的指数分布,各服务窗对顾客的服务时间分别服从参数为μi(k)的指数分布,且与顾客的到达时间间隔相互独立,其中下标i表示第i个服务窗;不同的是本文还假定每个服务窗的服务率μi(k)随系统队长k(系统中的顾客数)呈分段增长。针对这个模型,文中讨论了在n=2的情形下,运用系统的状态转移图列出K氏方程的方法,根据定理,若某生灭过程存在平稳分布,则该平稳分布应该满足K氏方程和正则性,通过求解K氏方程组,结合正则性条件,得到了系统队长的平稳分布。For the queueing model with the different ability of the windows, the findings of some studies are given in the condition that each window＇s service rate is stable. In order to meet the needs of real life, Queueing Model in this paper is established with the situa- tion that the abilities between the windows are different and the service rate is changeable, Given that the interval of customers＇arrival time obeys the exponential distribution with parameter m, the service time of various service windows obeys the exponential distribution with parameter μi （k） where the subscript i represents the first i-service window and is mutually independent with the interval of customer＇s arrival time; The difference is that the service rate μi（k） shows changes in the law of sub-growth with the system size k （the number of the customers in the system）. In view of this model, in the case of n = 2, get K＇s equations by the state transition graph. According to the theorem, if a steady distribution of a birth-death process exists, the steady distribution should satisfy K＇s equation and the regularity. When we solve them, we finally find the steady distribution of the system size.

关 键 词：排队模型 窗口能力不等 可变服务率 平稳分布 

分 类 号：O226[理学—运筹学与控制论]