Comment on “A general model for long-tailed network traffic approximation”

Abstract

The recent paper by Wang et al. (J. Supercomput. 38:155–172, 2006) proposed a Hyper Erlang model for long-tailed network traffic approximation. The paper argued that traditional models such as the Pareto, Weibull and log normal distributions are difficult to apply because of “their complex representations and theoretical properties”. The paper went on to say that the Pareto distribution “does not have analytic Laplace transform, and many other heavy-tailed distributions, such as Weibull and log normal also do not have closed-form Laplace transforms”.

In the following, we would like to show that one can actually derive explicit expressions for Laplace transforms of heavy-tailed distributions. The next three sections provide explicit expressions for the Laplace transforms of the Pareto, Weibull and the log-normal distributions. To the best of our knowledge, these are the first known results on Laplace transforms of heavy-tailed distributions.