This paper deals with the analysis of a two-phase MX/Ek/1 queuing system with N-Policy for exhaustive batch service with and without gating. Customers arrive in batches of random size according to a Poisson process and receive batch service in the first phase and individual service in the second phase. After providing the second phase of service to all the customers in the batch, the server returns to new customers who have arrived. If the customers are waiting, the server restarts the cycle by providing them batch service followed by individual service. In the absence of customers, the server takes a vacation and returns only after N customers join the queue to start the service. The explicit expressions for steady state distribution of the number of customers in the queue are obtained and also derived the expected system length. A cost model is developed to determine the optimum value of N. The expected system length is evaluated for the three bulk size distributions: Deterministic, Geometric and Positive Poisson based on assumed numerical values given to the system parameters. Sensitivity analysis is also investigated.
