带有两类顾客,服务台可修的M/G/1重试排队系统研究

An M/G/1 Retrial Queue with Two Types of Customers and Repairs

主要研究一类同时带有两类顾客,服务台可修的M/G/1重试排队系统。寻求服务的顾客分为两类:普通顾客和永久顾客。普通顾客和永久顾客在寻求服务时以概率p正常启动服务台并接受服务,以概率q启动失效并等待修理,服务台修理完成后继续寻求服务;普通顾客服务完成以后立刻离开服务台,永久顾客在服务完成以后,立刻回到重试组中继续寻求服务。给出系统稳态时的遍历条件,再利用补充变量法求解系统的稳态方程组,并且研究该系统的各项性能指标。

This paper relates to an M/G/1 retrial queue with two types of customers and repairs. Ordinary customers and Permanent customers, who could start the server successfully with probability p and starting failure with probability q and waiting for repair. Ordinary customers leave the system forever, who have received a service . Permanent customers, who immediately return to the Orbit after having received a service. We first present the ergodicity condition for the sys- tem to be stable and derive analytical results for the stationary distribution as well as some performance measures of the system by use the method of VMP.