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

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.

Copyright

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.

International Journal of Stochastic Analysis

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

Abstract

Copyright

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