Applicability of Transfer Function to Disturbance Growth Estimation and Traffic Stability

In linear stability analysis, some unrealistic assumptions (e.g., small and long wavelength disturbance) are made for the derivation of the transfer function, which may result in an inaccurate estimation of disturbance growth rate and incorrect judgment of traffic stability. To gain more insights into the relaxation of assumptions on disturbance, this paper studies the effect of disturbance magnitude and frequency on the accuracy of disturbance growth rate estimation and the applicability of transfer function to traffic stability. The disturbance growth rates of several car-following (CF) models, including both linear and nonlinear CF models, are examined through two-vehicle simulations. The calibrated growth rate is then verified with a simulation involving a long vehicle platoon. The simulation results demonstrate that the calibrated growth rate from a two-vehicle CF pair is applicable to predict the disturbance magnitude of a long platoon. In addition, a concave growth pattern is observed, for which a novel explanation is provided based on the traditional deterministic CF model for the first time.