具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．

The Discrete-time Queueing System with Repairable Server and Phase-type Repair Time

In this paper, the discrete-time queueing system with repairable server and a general independent input and phase-type repair time are studied. Suppose that service times of customers and lifetime of server follow geometric distributions, the distributions of stationary queue length and waiting time are provided by using the matrix analytic method, and these distributions are proved to be discrete phase-type distributions. We also obtain the distributions of failure number which server takes in a generalized service time, and show that it follows a modified geometric distribution. Furthermore, we provide a comparison on two queueing systems with same arrival processes, service times, lifetime of server and repair times but one is in a discrete version and the other is in a continuous version. Finally, the relationship among the arrival process, service time and failure rate of server are illuminated by several numerical examples.