It is well-accepted that Pareto (heavy-tailed) and Gamma (short-tailed) distributions can be used to model the on-off time of a bursty traffic. If $X$ is Pareto, i.e. $X\sim\dfrac{ac^a}{(x+c)^{a+1}}$, and $Y$ is Gamma, i.e. $Y\sim\dfrac{y^{\alpha-1}e^{-y/\lambda}}{\lambda^\alpha\Gamma(\alpha)}$, then $R=X+Y$ models the time between successive on-off cycles.

This paper proposed and proved the solution for the p.d.f. of $R$ as the convolution of the p.d.f. of Pareto and Gamma.

## Bibliographic data

@article{
title = "On the convolution of Pareto and gamma distributions",
author = "Saralees Nadarajah and Samuel Kotz",
journal = "Computer Networks",
volume = "51",
pages = "3650--3654",
year = "2007",
}