Analyzing the M/M/1 queue in frequency domain experiments

Frequency domain experiments are a method of performing sensitivity analysis and factor screening, and estimating gradients for steady-state simulation models. The validity of the frequency domain analysis can be assessed by measuring the distance between the expected outputs of the sinusoidally oscillated input parameter system (as found in frequency domain experiments) and the fixed input parameter system (as found in time domain experiments). In this paper, an upper bound on this distance is derived for an M/M/1 queue, as the oscillation frequencies of the sinusoidally varied input parameters approach zero. This bound is shown to converge to zero as the input parameter oscillation ranges approach zero. This bound is also related to a Taylor series approximation of the output response function, and shown to converge to zero at the same rate as this approximation function. In addition, this bound is used to assess the bias of the harmonic gradient estimator.