A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution

Cohen, J. W.

doi:https://doi.org/10.1155/S1048953398000215

International Journal of Stochastic Analysis

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Volume 11 |Article ID 149413 | https://doi.org/10.1155/S1048953398000215

J. W. Cohen, "A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution", International Journal of Stochastic Analysis, vol. 11, Article ID 149413, 8 pages, 1998. https://doi.org/10.1155/S1048953398000215

A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution

J. W. Cohen¹

¹CWI, P.O. Box 94079, Amsterdam 1090 GB, The Netherlands

Received01 Jul 1997

Revised01 Nov 1997

Abstract

For the GI/G/1 queueing model with traffic load a<1, service time distribution B(t) and interarrival time distribution A(t), whenever for t→∞1−B(t)∼c(t/β)ν+O(e−δt),c>0,1<ν<2,δ>0, and ∫0∞tμdA(t)<∞ for μ>ν, (1−a)1ν−1w converges in distribution for a↑1. Here w is distributed as the stationary waiting time distribution. The L.-S. transform of the limiting distribution is derived and an asymptotic series for its tail probabilities is obtained. The theorem actually proved in the text concerns a slightly more general asymptotic behavior of 1−B(t), t→∞, than mentioned above.

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Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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