Abstract:
Traffic oscillations have been the subject of intensive research since the 1950s. Originally, linear car-following laws were used to analyze oscillation properties, but more recently, nonlinear car-following laws have been used in order to reproduce more accurate car-following behavior. While calibrating the nonlinear laws with field data, however, most research focuses on matching vehicle trajectories in the time domain. Li et al. incorporated frequency domain properties (e.g., oscillation periodicity and amplitude) into car-following model calibration such that the describing-function approach (DFA) can be used to predict the oscillation behavior of a homogeneous platoon. No consideration was given to ensure prediction accuracy in both the time-and frequency-domains simultaneously. This paper proposes a new approach to calibrate the parameters in a driver-dependent nonlinear car-following law based on field trajectories. This method is shown to achieve a better balance between time- and frequency-domain trajectory properties. The developed calibration framework implements maximum likelihood estimation with a simulation-based feedback incorporating both time- and frequency-domain prediction errors. The likelihood estimator is obtained from a modified Tobit model to capture the nonlinearity of the car following model (e.g., because of truncation near zero or maximum speeds). The feedback is established by comparing the observed field trajectory with the simulated one under a certain car-following law, where their actual trajectories and frequency spectrums are used to compute their time- and frequency-domain errors, respectively. The car-following law is calibrated for each pair of leader-follower drivers, allowing researchers to consider a platoon of heterogeneous drivers. The DFA can then be used to predict oscillation propagation in a platoon.
