Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue

In this paper, we present an efficient numerical method for calculating the waiting time and idle time distributions of the arithmetic GI/G/1 queue. Our method is based on the Wiener-Hopf factorization, which is briefly reviewed. Compared to the related methods suggested in the literature, our method seems to perform very well, and it is often faster by several orders of magnitude. A number of numerical examples conclude the paper.