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Approximations for the GI/G/c queue

Published online by Cambridge University Press:  14 July 2016

M. H. Van Hoorn  and
L. P. Seelen
M. H. Van Hoorn
Affiliation:
Vrije Universiteit, Amsterdam
L. P. Seelen*
Affiliation:
Vrije Universiteit, Amsterdam
*
∗Postal address: Vrije Universiteit, Interfaculteit der Actuariële Wetenschappen en Econometrie, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
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Abstract

In this paper, we give good-quality approximations for multiserver queues with general service-time distributions. For the interarrival-time distribution we consider hyperexponential distributions and mixtures of Erlang distributions with the same scale parameters. We give an algorithm to compute various operating characteristics such as the delay probability and the mean queue length.

The approximations are obtained by making assumptions regarding the residual service times of services in progress at service completion epochs, whereas the arrival process is modelled exactly. As the operating characteristics are far more sensitive to changes in the parameters of the arrival process, the latter is very important.

The quality of the approximations is extensively tested by using the exact results of more than 2000 cases. In heavy traffic the average relative error is up to 1% and in moderate traffic about 4%.

Keywords

MULTISERVER QUEUEDELAY PROBABILITYMEAN QUEUE LENGTH
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 484 - 494
Copyright
Copyright © Applied Probability Trust 1986 

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