Functional Criticality of the Busy Period Distribution in the GI/G/1 Queue

摘要

We derive the asymptotic characterization of the busy period in the stableGI/G/1 queue with square root insensitive service time distributions. Asymptotically,the tails of these distributions are heavier than e~(-x(1/2)) and have zero relativedecrease in intervals of length x(1/2), hence square root insensitive. The result impliesthat the tail behavior of the busy period exhibits a functional change fordistributions that are lighter than ~(-x(1/2)).