具有两种故障状态的M/G/1可修排队系统

Analysis of the Repairable Queueing System M/G/1 with Two Kinds of Breakdown States

人们已对可修的M G 1排队系统做了大量的研究工作 ,但大多只研究了具有一种故障状态的可修排队系统 而笔者研究了具有两种故障状态 (正常和异常 )的M G 1可修排队系统 其中正常故障状态是由于服务台的寿命终止而引起系统失效 ,其修理时间为正常故障修理时间 ;异常故障状态是由于服务员操作失误等其他原因而造成系统失效 其修理时间为异常故障修理时间 假定服务台的寿命具有负指数分布 ,修理时间和服务时间均为一般分布

Much has been done concerning repairable queueing system M/G/1 and plenty of results been obtained. But those results are mainly concerned with the situation of only one kind of breakdown state. In this paper, we study the repairable queueing system M/G/1 with two kinds of breakdown states (normal and abnormal). Normal breakdown is caused by the life termination of the service station and abnormal breakdown results from the operation lapse. We propose that the life length of the service station has exponential distribution and the both normal and abnormal repair times have general distribution. By the method of Vector Markov Process, we obtain some characteristics of the system, main reliability indices of the service station, and important performance measures of the queue.