Large deviations of square root insensitive random sums Academic Article

abstract

• We provide a large deviation result for a random sum [Formula: see text], where Nx is a renewal counting process and {Xn}n0 are i.i.d. random variables, independent of Nx, with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than ex and have zero relative decrease in intervals of length 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 than ex.

authors

• Momcilovic, Petar

published proceedings

• MATHEMATICS OF OPERATIONS RESEARCH

author list (cited authors)

• Jelenkovic, P. R., & Momcilovic, P.

citation count

• 25

complete list of authors

• Jelenkovic, PR||Momcilovic, P

publication date

• January 2004

publisher

• Institute for Operations Research and the Management Sciences (INFORMS)  Publisher

published in

• Mathematics of Operations Research  Journal

keywords

• Busy Period
• Gi/g/1 Queue
• Large Deviation
• Random Sum
• Square Root Insensitivity
• Subexponential Distribution

Digital Object Identifier (DOI)

• 10.1287/moor.1030.0082

start page

• 398

end page

• 406

volume

• 29

issue

• 2

URL

• http://dx.doi.org/10.1287/moor.1030.0082