Large Deviations of Square Root Insensitive Random Sums

Authors:
Predrag R. Jelenkovic;Petar Momcilovic
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
2004

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Abstract

We provide a large deviation result for a random sum S Nxn=0 X n , whereN xis a renewal counting process and { X n } n=0are i.i.d. random variables, independent ofN x , with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier thane -vxand have zero relative decrease in intervals of length v x, hence square root insensitive. Using this result we derive the asymptotic characterization of the busy period distribution in the stable GI/G/1 queue with square root insensitive service times; this characterization further implies that the tail behavior of the busy period exhibits a functional change for distributions that are lighter thane -vx .