M/M/N Queue System with Balking Reneging and Server Breakdowns

In this paper we consider the system of M/M/N queue with server breakdowns plus balking and reneging,the rates of server breakdown are different from busy time and idle time,and there is one repairman in the system.We derive the steady state distribution of the number of effective servers,the moment generating function of the steady state queue length and the system performance measures.