Rate conservation law analysis of an M/G/1 type queue with repairable server

Using the Rate Conservation Law (RCL) method, developed from the stationary point processes and Palm distribution theory, we study a type of M/G/1 queueing system with repairable server of generally distributed lifetimes. After getting the steady-state workload and the pseudo-virtual waiting time expressions, we have obtained the first passage time to server failure, the probability of server availability, the mean of server failure probability, the mean times of server failure, and the failure rate of the system. It is interesting that some of them match with the known results in literature when the times of servers are exponentially distributed instead of general distributions.