具有两种服务速度的可修M^X/G(M/M)/1排队系统

Repairable M^X/G(M/M)/1 queueing system with two service speeds

在服务速度可变的M/G(M/M)/1可修排队系统的基础上,考虑顾客批量到达的情况,建立了一个具有两种服务速度的可修MX/G(M/M)/1排队模型.在这个批量到达的排队系统中,服务台具有两种服务速度.当系统中到达的第一批顾客数大于事先设定的正整数N时,服务台以较高的服务速度2服务顾客直到系统变空.当系统中到达的第一批顾客数小于或等于N时,服务台以较低的服务速度1服务顾客.如果服务台以较低的服务速度1服务顾客时再有顾客到达并且使得系统中的顾客数大于N,则从下一个顾客开始服务台以较高的服务速度2服务顾客直到系统变空.通过补充变量法得到了系统的状态转移图,根据状态转移图得到了系统的微积分方程组,然后对方程组求解得出了系统的队长分布及一些可靠性指标.

A batch arrival queueing system with two service speeds on the basis of repairable M/G（M/ M）/1 queueing system with changeable service speed is considered, and a repairable M^X/G（M/M）/1 queueing system with two service speeds is derived. In this batch arrival queueing system the sever can provide two service speeds： if the number of the batch customers in the system is more than N which is preset in the beginning, the sever provides service for the customers with higher speed 2 until there is no customer in the system; if the number of the batch customers in the system is less than or equal to N, the sever provides service for the customers with the lower speed 1. By the method of supplementary variable the state transition-rate diagram, the system of equations, the queue length and some reliability indexes are derived.