窗口能力不等、输入率可变且有差错服务的M/M/2排队模型研究

M/M/2 Queuing Model with Variable Input,Wrong Service and Different Ability of the Windows

主要研究了窗口能力不等、有差错服务且输入率可变的M/M/2排队模型。设顾客到达系统的时间间隔服从参数为λ的指数分布,二服务窗对顾客的服务时间分别服从参数为μ_1和μ_2的指数分布且与顾客到达时间间隔相互独立,当系统队长为k时,顾客进入系统同时排队等待的概率为α_k=1/k,窗口提供正确服务、不出差错概率为γ_k=k/k^a+1。基于排队系统的状态转移图推导出了K氏方程,同时考虑正则性条件,求得系统队长的平稳分布以及主要指标。

This paper discuss the M/M/2 queuing model with variable input, wrong service and different ability of the windows. Suppose the customers＇ arrival time interval obeys the exponential distribution with parameter;t, the 2 windows＇ service time obeys the exponential distribution with parameter μ1 and μ2 and is mutually independent with the interval of customers＇ arrival time. Suppose that the probability of customers joining the system is ak=1/k,consider the right probability of service is γk=k/k^a＋1.According to the state transition graph and K＇s equations, find the steady distribution and the main specifications of the system,