Optimal policy for bulk queue with multiple types of server breakdown

In this paper, an unreliable server M^X/M/1 queueing system with multiple types of server breakdowns under N‐policy is considered. Breakdowns occur only when the server is in busy state and each type of breakdown requires a random number of finite stages of repair. It is assumed that the lifetimes and phase repair time of the server for the individual stage are exponentially distributed. Matrix‐geometric method is employed to obtain the mean queue length and other system characteristics. We perform extensive numerical experiment to demonstrate the effect of various parameters on the system performance characteristics.