Empirical analysis and simulation of the evolution concavity of traffic oscillations

TL;DR

This study analyzes the growth pattern of traffic oscillations, revealing a universal concave evolution law through empirical data, experiments, and simulations, challenging traditional convex disturbance growth models.

Contribution

It uncovers a universal concave growth pattern of traffic oscillations and demonstrates that stochastic 2D models can accurately reproduce this behavior.

Findings

Velocity standard deviation increases concavely along vehicles.

Empirical and experimental results collapse into a single concave curve.

Stochastic 2D models reproduce the concave growth pattern.

Abstract

This paper has investigated the growth pattern of traffic oscillations in the NGSIM vehicle trajectories data, via measuring the standard deviation of vehicle velocity involved in oscillations. We found that the standard deviation of the velocity increases in a concave way along vehicles in the oscillations. Moreover, all datasets collapse into a single concave curve, which indicates a universal evolution law of oscillations. A comparison with traffic experiment shows that the empirical and the experimental results are highly compatible and can be fitted by a single concave curve, which demonstrates that qualitatively the growth pattern of oscillations is not affected by type of bottleneck and lane changing behavior. We have shown theoretically that small disturbances increase in a convex way in the initial stage in the traditional models presuming a unique relationship between speed and density, which obviously deviates from our findings. Simulations show that stochastic models in which the traffic state dynamically spans a 2D region in the speed-spacing plane can qualitatively or even quantitatively reproduce the concave growth pattern of traffic oscillations.