Abstract
We study the tail asymptotics of the r.v. X ( T ) where { X ( t )} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail of X ( T ) is sensitive to whether or not T has a heavier or lighter tail than a Weibull distribution with tail e − x . This leads to two distinct cases, heavy tailed and moderately heavy tailed, but also some results for the classical light-tailed case are given. The results are applied via distributional Little ’ s law to establish tail asymptotics for steady-state queue length in GI/GI/1 queues with subexponential service times. Further applications are given for queues with vacations, and M/G/1 busy periods.
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