具有强占优先权的不耐烦顾客的M/M/m/k排队模型

首先研究只有一类不耐烦顾客的M/M/m排队模型,其中顾客到达服从相互独立的泊松分布,服务时间服从相互独立的指数分布,到达率与服务率随着系统中的顾客数而发生变化。顾客的耐心等待时间(截止到服务开始前)服从指数分布。在此基础上进一步研究两类顾客到达的M/M/m/k排队系统。其中第一类顾客对于第二类顾客有强占优先权,两类顾客的到达率与服务率随着系统中顾客人数而发生变化。采用矩阵分析的方法得到了两类顾客各自的稳态分布,并有相应的性能分析,为系统的优化设计提供了依据。

M/M/m/k queue with preemptive resume and impatience of the prioritized customers

This article gives the result of M/M/m queue systems with one-class alone customers first,of which the customer-arrival is subordinate to the independent poisson distribution each other,the service-time the exponential distribution,and the arrival rate and the cumulative service rate will change with the number of customers in the system,but the service rate is assumed to be a constant.Further,this article studies the M/M/m/k queueing systems where there are two-class customers.The first class customers have the preemptive priority and exponential customer impatience.The queue length distribution in stationary state and performance measures are gained by using the method of matrix analysis.