On M/M/1 queues with a smart machine

On M/M/1 queues with a smart machine

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Article ID: iaor19992895
Country: United States
Volume: 24
Issue: 1/4
Start Page Number: 23
End Page Number: 36
Publication Date: Feb 1996
Journal: Queueing Systems
Authors: , , ,
Keywords: M/M/1 queues
Abstract:

This paper discusses a class of M/M/1 queueing models in which the service time of a customer depends on the number of customers served in the current busy period. It is particularly suited for applications in which the server has some kind of learning ability and warms up gradually. We present a simple and computational tractable scheme which recursively determines the stationary probabilities of the queue length. Other performance measures such as the Laplace transform of the busy period are also obtained. For the first N exceptional services model which can be considered as a special case of our model, we derive a closed-formula for the generating function of the stationary queue length distribution. Numerical examples are also provided.

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