带随机启动时间与双阈值(m,N)-策略的M/G/1可修排队系统的最优控制策略

Optimal Control Policy for the M/G/1 Repairable Queueing System with Random Start-up Time and Bi-level Threshold(m,N)-Policy

本文研究带随机启动时间与双阈值(m,N)-策略的M/G/1可修排队系统,首先讨论系统有关的排队指标,接着研究因为故障而产生的系统的下列可靠性指标,如:服务台首次失效前的寿命分布、不可用度和(0,t]时间内的平均故障次数。最后,在建立费用模型的基础上,结合实际中检测公司检测样品的这一现实情况,研究了双阈值最优控制策略(m*,N*),并在同一组参数下与服务台不发生故障时系统的双阈值最优控制策略进行了比较。

This paper is concerned with M/G/1 repairable queueing system with random start-up time and bi-level threshold(m,N)-strategy.Firstly,some related queueing indices of the system are analyzed.Then,we study the following reliability indices of the system caused by faults,for example,the distribution function of the first failure time,the probability of the system failure,and the expected failure number within a time interval(0,t]。Finally,on the basis of the established cost model and combined with the actual situation of the company’s testing samples,we study the optimal control strategy of double threshold(m*,N*),as well as compare the optimal control policy of the queueing system under which the service station doesn’t fail.