Department of Electrical Engineering Technical Report Large Deviations of Square Root Insensitive Random Sums Large Deviations of Square Root Insensitive Random Sums
Department of Electrical Engineering Technical Report Large Deviations of Square Root Insensitive Random Sums Large Deviations of Square Root Insensitive Random Sums
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电气工程系技术报告平方根不敏感随机和的大偏差平方根不敏感随机和的大偏差
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通讯作者：
Petar Momčilovi´c
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作者：
P. Momcilovic;P. Jelenkovic;P. Jelenkovi´c;Petar Momčilovi´c
本系列中的技术报告被认为是半正式的。所表达的想法完全是作者的想法，有关内容的问题应直接向他们提出。本文给出了随机和Nxn =0 Xn的一个大偏差结果，其中Nx是更新计数过程，{Xn} n≥0是独立同分布的。随机变量，独立于N x，具有属于一类平方根不敏感分布的公共分布。渐近地，这些分布的尾部比e − x重，并且在长度为x的区间内相对减少为零，因此平方根不敏感。利用这一结果，我们得到了服务时间对平方根不敏感的稳定GI/G/1队列中的忙碌期分布的渐近特征;这一特征进一步表明，对于比e − 1x轻的分布，忙忙碌期的尾部行为表现出函数变化。
The technical reports in this series are considered to be semi-formal. The ideas expressed are solely those of the authors, and questions about the content should be directed to them. Abstract We provide a large deviation result for a random sum N x n=0 X n , where N x is a renewal counting process and {X n } n≥0 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 − √ x 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 e − √ x .