Comments on "Scalable Services via Egress Admission Control

In the recent paper by Cetinkaya et al , admission control tests are derived by approximating the sum of two Gumbel distributed random variables by a Gumbel distributed random variable. In fact, the sum of two Gumbel distributed random variables does not follow a Gumbel distribution. Here, explicit expressions are derived for the probability density function (pdf) and the cumulative distribution function (cdf) of the exact distribution of the sum. The discrepancy between the exact and the approximate distributions is studied numerically.