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The mean waiting time of a GI/G/1 queue in light traffic via random thinning

Published online by Cambridge University Press:  14 July 2016

Soracha Nananukul*
Affiliation:
University of Massachusetts at Amherst
Wei-Bo Gong*
Affiliation:
University of Massachusetts at Amherst
*
Postal address: Department of Electrical and Computer Engineering, University of Massachusetts at Amherst, Amherst, MA 01003, USA.
Postal address: Department of Electrical and Computer Engineering, University of Massachusetts at Amherst, Amherst, MA 01003, USA.

Abstract

In this paper, we derive the MacLaurin series of the mean waiting time in light traffic for a GI/G/1 queue. The light traffic is defined by random thinning of the arrival process. The MacLaurin series is derived with respect to the admission probability, and we prove that it has a positive radius of convergence. In the numerical examples, we use the MacLaurin series to approximate the mean waiting time beyond light traffic by means of Padé approximation.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1995 

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