具有两种服务和多重延误休假的可修M^X/(G_1+G_2)(M/M)/1排队系统

The Repairable M^X/(G_1+G_2)(M/M)/1 Queuing System with Two Phases of Service and Multiple Delay Vacations

在批量到达的可修排队系统的基础上,考虑服务台提供两种不同服务的情况.第一种服务完成后紧接着进行第二种服务,第二种服务完成后顾客离开系统.并将多重延误休假引入该系统中,如果服务员发现系统中没有顾客时,并不立即休假,而是有一段准备时间,在此期间内如果有顾客到达则终止休假准备立即为顾客服务,否则服务员开始休假.通过补充变量法得到了系统的瞬态队长母函数,稳态队长母函数和系统的一些可靠性指标.

A batch arrival queuing system with two heterogeneous services is studied. In the system, the first phase service is followed by the second phase service, and a customer will leave the system after completion of both phases of service. The system with multiple vacations is considered as well, if there is no customer in the system, the server doesn＇t go for a vacation at once, but waits for a moment. If a customer arrives during the stage, the server stops going for a vacation and serves the customer, other- wise it will go for a vacation. By the method of supplementary variable, the queue length and some reliability indexes are derived.