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

Part of: Special processes Approximations and expansions Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Soracha Nananukul  and
Wei-Bo Gong
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.
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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.

Keywords

MACLAURIN SERIESWAITING TIMEPADÉ APPROXIMATION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 256 - 266
Copyright
Copyright © Applied Probability Trust 1995 

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