Nadarajah and Kotz (2007) On the convolution of Pareto and gamma distributions (ComNet(51))
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.
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