On the convolution of Pareto and gamma distributions

It is well established that the burst and idle times for on/off traffic are modeled by the Pareto and gamma distributions, respectively. Thus, the inter arrival times between on-traffic (off-traffic) is the convolution of Pareto and gamma random variables. In this note, we derive exact expressions for the probability density function of the inter arrival times. A computer program and tabulations of the associated percentage points are also provided.