Analysis of a Discrete-Time Queueing System with an NT-Policy

Abstract

In this paper, we analyse a discrete-time single-server queue operating under the NT-policy, which aims at clustering the service of customers in order to reduce the number of server activations and deactivations. Starting from an empty queue, the service of arriving customers is postponed until either of two thresholds is reached. Specifically, exhaustive service of customers is initiated only if either N customers have accumulated (space threshold) or if more than T slots have passed since the arrival of the first customer. This way, the queue cycles between three states, i.e. an empty phase, an accumulating phase and a serving phase. A Bernoulli arrival process and deterministic service times are assumed. We derive the steady-state probabilities of the system’s state as well as the distributions of the phase sojourn times and the customer delay. For the latter, we condition on the phase during the customer’s arrival slot. The influence of the model parameters on the results is discussed by means of a numerical example.