Summary: This investigation analyzes a breakdown service with setup time under \(N\)-policy. Only in working condition, the server may fail and dispatch immediately for the repair job which can be performed according to exponential distribution by a repairman. The server goes on vacation if the system does not have job to perform, i.e., the system is empty and later on switches on when the system accumulates \(N\) jobs. The arrivals at service station of the customers follow Poisson fashion with rate dependent on the server’s status which may be idle, busy or broken-down state. By using generating function method, we derive the queue size distribution. The expressions for various performance characteristics including average queue length, probabilities of long-term fraction of time for which the server is idle, busy, broken down and in repair state. The optimal value of threshold parameter \(N\) which minimizes the total average cost is determined analytically. The parameters’ sensitivity on different performance measures is examined by facilitating the numerical results.