In this study, we analyze two-phase queueing systems with N-policy. Customers arrive at the system according to a Poisson process. They receive a batch service in the first phase and individual services in the second phase. Both service times are assumed to have general distributions. If the system becomes empty at the completion of the second phase, the server turns to be idle until the queue length reaches N. Specifically, we consider two cases of this system. One is the Gated Batch Service Case, where customers arriving during the batch service have to wait until the next batch service starts. The other is the Exhaustive Batch Service Case, where customers arriving during the batch service join the current batch in service. For both cases, we derive the steady-state system size and sojourn time distributions. In addition, we present the server utilization and the system operation cost in the gated batch service case.
