The impact of the NT-policy on the behaviour of a discrete-time queue with general service times

In this paper, we analyse the behaviour of a discrete-time singleserver queueing system with general service times, equipped with the NTpolicy. 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.

Publication year:2014

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IOF-keylabel:yes

BOF-publication weight:0.1

CSS-citation score:1

Authors:National

Authors from:Higher Education

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