Indicator Random Variables in Traffic Analysis and the Birthday Problem

This paper proposes using collisions of Pareto random variables in traffic analysis and in generating fictitious network traffic that follows various Pareto distributions. Pareto distributions are commonly found in network statistics, but the distributions may be truncated or overlapping, thus making it hard to estimate their sample parameters. Therefore, this paper investigates methods of computing parameters of binned collisions of Pareto random variables. This paper explores an indicator variable approach to analyzing collisions of Pareto random variables. These collisions are initially modeled by the birthday problem or paradox and then they are extended to understand independence of collisions. This paper´s use of indicator variables simplifies the calculation of higher moments for binned collisions of Pareto random variables