International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 149413 | 8 pages | https://doi.org/10.1155/S1048953398000215

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

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 t1B(t)c(t/β)ν+O(eδt),c>0,1<ν<2,δ>0, and 0tμdA(t)< for μ>ν, (1a)1ν1w converges in distribution for a1. 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 1B(t), t, than mentioned above.

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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