A recursive method for the N policy GI/M/1 queueing system with finite capacity

This paper studies a single removable server in a GI/M/1 queueing system with finite capacity operating under the N policy. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distributions of the number of customers in the system. The method is illustrated analytically for exponential interarrival time distribution. Numerical results for various system performance measures are presented for four different interarrival time distributions such as exponential, 2-stage hyperexponential, 4-stage Erlang, and deterministic.