Iterative Computation of the M/G/1 Queue Length Distribution via the Discrete Fourier Transform

An iterative method is presented by which the distribution of queue lengths in the M/G/1 queue may be computed. The method applies to the nonsteady-state case and involves repeatedly performing convolutions. The steady-state solution may be obtained by performing the iterations until convergence occurs. A frequencydomain equivalent of the method is presented which gives much greater computational economy.