Analysis of M/M/1 queueing systems with negative customers and unreliable repairers

In this article, we study the M/M/1 queueing systems with negative customers and unreliable repairers. The arrival of a negative customer causes the failure of the server, and the server is repaired immediately. The repairers may successfully repair the server with probability p, and the server continues to serve customers in the system. Otherwise, once the repair fails, the system will be cleared and all customers are forced to leave the system. By analyzing the quasi-birth-and-death process and using the probability generating function method, we obtain the steady-state probability and some performance measures of the system. Then, based on the reward-cost structure, we discuss the strategic behavior of customers and consider the equilibrium strategy. Finally, the effects of system parameters on the performance measures, individual benefit, and social benefit are analyzed by numerical examples.