Large deviations of square root insensitive random sums

• 成果类型: Article
• 署名作者: Jelenkovic, PR; Momcilovic, P
• 署名单位: Columbia University; International Business Machines (IBM); IBM USA
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1030.0082
• 发表日期: 2004
• 页码: 398-406
• 关键词: independent random-variables; reduced-load equivalence; integral limit theorems; cramers condition; busy period; Heavy Tails; asymptotics; distributions; probabilities; BEHAVIOR

摘要

We provide a large deviation result for a random sum Sigma(n=0)(Nx) X-n, where N-x is a renewal counting process and {X-n}(ngreater than or equal to0) are i.i.d. random variables, independent of N-x, with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than e(-rootx) and have zero relative decrease in intervals of length rootx, 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 e(-rootx).