多服务窗等待制M/M/n排队模型  

M /M /n Queue Model of Multi Service Window Waiting System

作　　者：付馨雨[1] 罗国旺[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆理工大学学报（自然科学）》2013年第12期139-142,共4页Journal of Chongqing University of Technology：Natural Science

摘　　要：李焕研究了当系统中的对长为k时,新来的顾客以概率αk=1/(k+1)加入系统,当排队等待的队长为k时,不耐烦顾客以强度Δk=k2δ(δ≥0)离开队伍的具有可变输入率和不耐烦顾客的M/M/n排队模型。推广了该结论,将具有两类服务率的M/M/n排队模型与上述2个模型进行了结合研究,并考虑了顾客的实际情况,即选择来到服务窗口说明顾客至少需要这种服务。通过对生率和灭率函数的改进,建立了输入率可变且具有两类服务率及不耐烦顾客的M/M/n排队模型,得到了模型的平稳分布以及各项重要指标,该研究结果具有实际意义。LI Huan discusses that in the system when the captain is k, new coming customers join the 1 system with probability of ak = 1/k＋1. And when the waiting captain in queue is k, impatient custom-ers depart from the queue with intensity△k=k^2δ（δ≥0）, which is provided with variable input rate and impatient customers＇ M/M/n queue model. This thesis popularizes the related conclusions of LI Huan, in which an integrated study is made to discuss the M/M/n queue model with two types of service rate and the above-mentioned two models. Moreover, the thesis takes the practical situation of customers into account. The customers choosing the service window means they need this service. Thus the variable input rate and impatient customers＇ M/M/n queue model with two types of service rate are constructed by means of the improvement of birth rate and out the rate function. Therefore, the stationary distribution and important indicator of this model can be received. This research has a practical significance.

关 键 词：可变输入率 可变服务率 不耐烦顾客 M M n排队模型 

分 类 号：O21[理学—概率论与数理统计]