伴有故障和延迟维修的清空排队系统的均衡分析

Equilibrium analysis for a clearing queueing system with breakdowns and delayed repairs

考虑一个马氏排队清空系统,将其看成一个在站台服务的容量无限的交通服务系统,顾客按照泊松过程到达系统后接受服务,而服务时间服从指数分布,假设交通工具容易出现故障,并且经过一个服从指数分布的延迟时间后,才能得到修理.在几乎可见情形下,顾客根据前面已进入系统的人数决定是否进入系统,结合一个线性支付函数,获得了顾客的均衡离开策略.

We consider a single server clearing queueing system,which may simulate the arrivals of a transportation facility with unlimited capacity at a platform.The customers arrive the system according to a Poisson process and the service times are exponentially distributed.The facility is subject to breakdowns and can only be repaired after an exponentially distributed delay time.In almost observable case,customers have option to decide whether to join or balk the queue based on observation of the length of queue.Using a natural linear reward-cost structure,we obtain the balking strategy behavior of customers.