输入率和服务率可变且窗口能力不等的M/M/n排队模型研究  

M/M/n Queuing Model with Variable Input and Service Rate and Different Ability of the Windows

作　　者：冀云[1] 高世泽[2] 

机构地区：[1]重庆电子工程职业学院应用电子学院,重庆401331 [2]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2014年第3期65-67,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家社会科学基金(No.13BTJ008)

摘　　要：本文建立了窗口能力不等且输入率和服务率可变的M/M/n排队模型。设顾客到达队列的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到达时间间隔相互独立。本文还假定随着系统队长k的增加,顾客加入队列的概率减小;各服务窗服务率μi(k)随队长k呈快慢两档变化。重点讨论了该模型n=2的情况,运用系统的状态流图列出K氏方程,结合正则性条件,得到了系统队长的平稳分布。Combining the actual situation, Queuing Model is established with the situation that the service abilities between the win- dows are different and the input and service rate are changeable, suppose that the interval of customers arrival time obeys the expo- nential distribution with parameter X, the service time of various windows obeys the exponential distribution with parameter μi （k） and is mutually independent with the interval of customers＇ arrival time. Given that with the increase of queue length, the probabil- ity of customer join the system might decrease; the service rate μi （k） shows changes in two-grade with the system size. As to this model, in the case of n= 2, get K＇ s equations by the state transition graph according to the regularity, finally find the steady distri- bution of the system size.

关 键 词：排队系统 输入率可变 服务率可变 窗口能力不等 

分 类 号：O226[理学—运筹学与控制论]