带延迟修理的退化服务台排队系统更换模型研究

Research on Replacement Model for Queuing System with Deteriorative Repairable Service Station Including Delay Repair

针对带有延迟修理的退化可修服务台的排队系统,提出了一种新的维修更换模型。假定服务台逐次故障后的维修时间构成随机递增的几何过程,工作时间构成随机递增的几何过程,在服务台每次故障以概率p需要延迟修理和延迟修理时间为随机变量的情况下,选取被服务的顾客数N为其更换策略,以系统长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式。并根据目标函数情况,通过最大化目标函数来获取系统最优的更换策略N*,最后还对结果进行了讨论。

To study queueing system with deteriorative repairable service station including delay repair, this paper proposes a kind of new maintenance and replacement model. Supposing that the successive survival time of the system constitute a decreasing geometric process stochastically, while the consecutive repair time of the system constitute an increasing geometric process, under the conditions that the delay repair time is random variable and the failure service station needs delay repair with probability , we take the number N of the customer that have been serv- iced at the service station as its replacement policy and choose the long - run expected profit per unit time as objec- tive function. By using renewal process and geometric process theory, mathematic model is established and the ex- plicit expressions of the objective function is derived. According objective function, the optimal replacement policy is obtained by maximizing the objective function. Finally, we discuss the result also.