Random Environment Repairable Queuing System

In this thesis, a few kinds of queue systems which can be repaired are considered in stochastic environment.When catastrophic failure occurs in the systems occasionally, all current customers are missed (including waiting and served customers). Then the repairing process goes on immediately, and the systems can be back into normal status after a negative exponential repairing time. While when the systems are breakdown, new customers are become inpatient: every independent customer is according to a stochastic tolerant time, and he will give up waiting and never go back, if the time comes earlier than that of being repaired successfully. When the systems turns into being repaired, the customer arrival rate becomesλ0. While when the systems turns into work, the arrival rate and service rate ought to be adjusted with the Markov process in the stochastic environment.The queue systems of M/M/1, M/M/c and M/M/∞with stochastic environment are investigated. By models analysis and calculations, we derive the probability generating function, the corresponding queue length, and mean sojourn time of served coustomers. Finally, the conclusions are applied to cases of single work status and non customer arrival after breaking down.