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A second-order heavy traffic approximation for the queue GI/G/1

Published online by Cambridge University Press:  01 July 2016

Julian Köllerström
Julian Köllerström*
Affiliation:
University of Kent
*
∗Postal address: Mathematical Institute, University of Kent, Canterbury, Kent, CT2 7NF, U.K.
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Abstract

A second-order heavy traffic approximation for the stationary waiting-time d.f. G for GI/G/1 queues is derived, the first-order term of which is Kingman's (1961), (1962a), (1965) exponential approximation. On the way to this result there are others of independent interest, such as a convolution equation relating this waiting time d.f. G with the d.f. of a related ladder height, an integral equation for G and some stochastic bounds for G. The main result requires a particular type of functional convergence that may also be of interest.

Keywords

QUEUE GI/G/1WAITING TIMEHEAVY TRAFFIC APPROXIMATIONSSECOND-ORDER TERMSTOCHASTIC BOUNDSINTEGRAL EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 167 - 185
Copyright
Copyright © Applied Probability Trust 1981 

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