具有顾客重试机制的M/M/1可修排队模型及应用  

A Repairable M/M/1 Queueing Model With Customers' Retrial Behavior and its Applications

作　　者：侯利君[1] HOU Li -jun(Xinzhou Teachers University,Xinzhou 034000,China)

机构地区：[1]忻州师范学院,山西忻州034000

出　　处：《忻州师范学院学报》2018年第5期1-8,共8页Journal of Xinzhou Teachers University

摘　　要：文章研究的排队模型是在经典的M/M/1模型基础上加上顾客重试和系统故障。首先,基于经典的M/M/1模型理论提出带有顾客重试机制的M/M/1可修排队模型,利用马尔科夫理论以及生灭过程理论给出所要研究的系统的状态转移图和稳态方程,通过母函数法和递推法对方程进行求解得出系统的稳态概率;其次,通过得出的系统稳态概率进而可得到服务台处于不同状态时系统的概率母函数和状态概率,系统的平均队长等数量指标。再通过MATLAB软件进行数值实验来研究模型的参数变化对系统主要性能指标的影响。The queuing model to be studied in this paper is based on the classic M/M/1 model including customers’retrial behavior and system failure.Firstly,based on the classical M/M/1 model,this paper proposes a repairable M/M/1 queueing model with customer retry mechanism,the state transition diagram and the steady-state equations of the system to be studied are given by using the Markov theory and the theory of birth and death.The steady-state probability of the system are obtained by solving the equations by the generating function method and the recursion method.Furthermore,by deriving the steady-state probability of the system,when the service desk is in different states,we can get the probability generating functions of the system,the state probability of the system,the average queue length of the system and so on.And then through the MATLAB software to carry out numerical experiments to study the model parameters of the system on the main performance indicators.

关 键 词：重试排队系统 可修排队系统 马尔可夫过程 母函数 

分 类 号：O226[理学—运筹学与控制论]