THE IMPACT OF THE NT-POLICY ON THE BEHAVIOUR OF A DISCRETE-TIME QUEUE WITH GENERAL SERVICE TIMES

摘要

In this paper, we analyse the behaviour of a discrete-time single-server queueing system with general service times, equipped with the NT-policy. This is a threshold policy designed to reduce the number of service unit activation/deactivation cycles, whilst ensuring an acceptable delay trade-off. Once the server is deactivated, reactivation will be postponed until either N customers have accumulated in the queue or the first customer has been in the queue for T slots, whichever happens first. Due to this modus operandi, the system circulates between three phases: empty, accumulating and serving. We assume a Bernoulli arrival process of customers and independent and identically distributed service times. Using a probability generating functions approach, we obtain expressions for the steady-state distributions of the phase sojourn times, the cycle length, the system content and the customer delay. The influence of the threshold parameters N and T on the mean sojourn times and the expected delay is discussed by means of numerical examples.