On upper bounds for the tail distribution of geometric sums of subexponential random variables

Authors:
Andrew Richards
Affiliations:
Department of Actuarial Mathematics and Statistics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK
Venue:
Queueing Systems: Theory and Applications
Year:
2009

Citing 1
Cited 1

Tails of waiting times and their bounds

Queueing Systems: Theory and Applications

How to measure the accuracy of the subexponential approximation for the stationary single server queue

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several improvements and one correction are made, which enables the constructed bound to be significantly tighter. Several examples are given, showing how to implement the theoretical result.