Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 247-254

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

J. W. Cohen

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

Received 1 July 1997; Revised 1 November 1997

Copyright © 1998 J. W. Cohen. 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.


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.