QUEUE LENGTH DISTRIBUTIONS FROM PROBABILITY GENERATING-FUNCTIONS VIA DISCRETE FOURIER-TRANSFORMS

We review the relationship between the Discrete Fourier Transform (DFT) coefficients and the probability masses. We demonstrate that choosing a larger value for K does not necessarily improve the quality of the results when the objective is to obtain mass probabilities in queueing systems; instead, choosing an unnecessarily large K simply leads both to longer computation times and increased round-off error. We propose an alternative approach which takes advantage of the fact that the tail probabilities in queueing systems decay geometrically. Our approach addresses aliasing error and round-off error simultaneously and, in addition, provides tail probabilities.