  The main purpose of this note is to point out the relevance of the
Mittag-Leffler probability distribution in the so-called thinning theory for a
renewal process with a queue of power law type. This theory, formerly
considered by Gnedenko and Kovalenko in 1968 without the explicit reference to
the Mittag-Leffler function, was used by the authors in the theory of
continuous random walk and consequently of fractional diffusion in a plenary
lecture by the late Prof Gorenflo at a Seminar on Anomalous Transport held in
Bad-Honnef in July 2006, published in a 2008 book. After recalling the basic
theory of renewal processes including the standard and the fractional Poisson
processes, here we have revised the original approach by Gnedenko and Kovalenko
for convenience of the experts of stochastic processes who are not aware of the
relevance of the Mittag-Leffler function
