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

[摘要] For theGI/G/1queueing model with traffic loada<1, service time distributionB(t)and interarrival time distributionA(t), whenever fort→∞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−1wconverges in distribution fora↑1. Herewis 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 of1−B(t),t→∞, than mentioned above.

[学科分类] 应用数学