Waiting time distribution in an retrial queue

This paper analyzes the waiting time distribution in the M / PH / 1 retrial queue. We give expressions for the Laplace–Stieltjes transform of the waiting time. We then provide a numerical algorithm for calculating the Laplace–Stieltjes transform of the waiting time. Numerical inversion of the Laplace–Stieltjes transforms is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.