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Queue is due to the limited resources generally services related to limited server. Queueing theory with N-policy has the characteristics in which the server will use the time to be unemployed to perform other tasks that require the server to leave the system when there is no customer service and will be active in the service back after there is a number N of customers waiting to be served. In this research proposal, the researcher will analyze the two-phase queuing system service using the model M/M/1. There is a server (single server) serving customers in groups in phase 1 followed by individual services in phase 2. The system considers the state of the server queue is slow and customers are impatient. Characteristics server queuing system model of the N-policy M/M/1 with two phases of service in this research proposal raises the queuing system is divided into six states. Model analysis performed to obtain the probability of occurrence of each state, the expected number of customers, and the customer waiting time in the system. Further simulations to analyze the sensitivity of the value of N to parameters on the total cost function in order to get the optimal value of N that minimize the total cost.