Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws

A recent study (Li and Ouyang, 2011) proposed a describing-function approach (DFA) to analytically predict oscillation propagation properties (i.e., dominating frequency and amplitude growth) for a general class of nonlinear car-following laws. This paper presents a new graphic solution approach to DFA and proposes a systematic framework to validate DFA using observed vehicle trajectory data. A set of new empirical measures are defined to extract steady-state traffic properties and oscillation characteristics from vehicle trajectory data. A frequency-domain calibration approach based on DFA is developed to construct a proper nonlinear car-following model that fits these empirical measurements. The analytical DFA predictions of oscillation propagation patterns of the calibrated car-following law are then compared with (i) the observed oscillation properties, and (ii) the simulated oscillation characteristics from the same car-following law. Empirical experiments with real-world trajectory data show that the prediction, the simulation, and the field observation typically match very nicely. This not only validates the analytical prediction approach in the previous study, but also shows that the framework proposed in this paper is capable of calibrating a realistic nonlinear car-following law that reproduces the observed oscillation propagation phenomenon. Our proposed modeling method also brings theoretical analyses and empirical observations into one integrated framework that potentially lays the foundation to understand how nonlinearities in a car-following law affect traffic oscillation evolution, and develop possible counteracting strategies.