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The impact of the \(NT\)-policy on the behaviour of a discrete-time queue with general service times. (English) Zbl 1277.60151

Summary: 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.

MSC:

60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research
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