具有优先权的M／G／1重试可修排队系统

M/G/1 Retrial Queue System with Priority and Repair

在服务台忙的情况下,到达服务台的顾客以概率q进入无限位置的优先队列而以概率p进入无限位置的重试轨道(orbit),并且按照先到先服务(FCFS)规则排队,假定只有队首的顾客允许重试,同时考虑服务台可修的因素,证明了系统稳态解存在的充要条件.利用补充变量法求得稳态时两个队列与系统的平均队长、顾客等待时间、服务台的各种状态概率以及可靠性指标.

Arriving customers who find the server busy join the infinite priority queue with probability q and join the infinite retrial group （orbit） with complementary probability p in accordance with an FCFS discipline. The necessary and sufficient condition for the stability of the system is obtained, assuming that only the customer at the head of the orbit is allowed to retry for service and considering the factor of server breakdowns. The steady-state distributions of the numbers of customers in the priority queue, the orbit, and the system are obtained, along with average waiting times with the method of VMP. The main reliability indices of server, the probability that the server is idle, the service and the repair are also derived.