Computing the Waiting Time Distribution for the G/G/1 Queue by Signal Processing Methods

Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline. The first method is based on the use of the fast Fourier transform (FFT) for producing iterative solutions to a discrete version of Lindley's integral equation for both nonsteady state and equilibrium conditions. The second method makes use of the complex cepstrum, implemented with the FFT, for providing direct solutions with the queue in equilibrium.