Characterizing a nonstationary M/G/1 queue using Bode plots

A frequency-domain simulation experiment (FDE) is a discrete-event simulation experiment in which selected system parameters are oscillated sinusoidally to induce oscillations in one or more system response statistics of interest. A spectral (Fourier) analysis of these induced oscillations is then performed to gain valuable information about the system. FDEs are based upon an intuitive frequency invariance assumption-if a particular system response statistic is sensitive to a system parameter, then sinusoidal variation of that system parameter at a fixed frequency will induce similar sinusoidal variations in the system response statistics, at the same frequency. We provide some theoretical and experimental support for this FDE model assumption as it applies to a nonstationary M/G/1 queue with sinusoidally varying arrival rate and fixed service rate. Specifically, an analytical expression for the departure rate (system frequency response) is provided which verifies frequency invariance and quantifies the extent to which the induced sinusoidal variation is amplitude-modulated and phase-shifted relative to the arrival rate. An FDE method to generate Bode plots for a nonstationary M/G/1 queue with sinusoidally varying arrival rate and fixed service rate is presented. The FDE-generated Bode plots are compared with the analytical frequency response expression. In this way, we demonstrate that a nonstationary M/G/1 queue is characterized as a low-pass filter.