Analytical and computational aspects of the infinite buffer single server N policy queue with batch renewal input

Abstract

In this paper we provide a complete analysis of an infinite buffer batch arrival GIX/M/1 queue with N threshold policy. According to this policy, as soon as the system becomes empty, the server stops service and turns into an idle state. It again resumes service when the number of customers in the queue reaches N or more. Based on the supplementary variable and the difference equation method, we propose an algorithm to obtain the steady-state probability distribution of the system-size at pre-arrival and arbitrary epochs. We perform the waiting time analysis of the model and derive the mean waiting time of an arbitrary customer along with other performance measures. Finally, we validate our analytical results by some numerical examples and conduct certain numerical experiments to study the impact of parameters on the performance characteristics of the system. The work carried out in this paper provides a substantial methodological contribution in dealing with N policy queueing models, particularly with renewal arrival process.