Traffic dynamics modeling with an extended S3 car-following model

In recent decades, there has been a notable surge in research attention on microscopic car-following modeling, reflecting its indispensable role in investigating and simulating human driving behavior. Breakthroughs in operations research and machine learning have reinvigorated scholarly interest in addressing intricate traffic flow issues encountered in real-world scenarios. This study advances the current state of traffic dynamics modeling by presenting a novel extended S-shaped three-parameter (ES3) car-following model, achieving a harmonious balance between empirical accuracy and mathematical simplicity while enabling macroscopic-microscopic integration. Both local and string stability conditions of the ES3 model are derived and corroborated by numerical experiments. Utilizing real-world and autonomous vehicle trajectory data, we calibrate and validate the ES3 model using three distinct methodologies: single-vehicle microscopic model calibration, multi-vehicle microscopic model calibration, and integrated self-consistent macroscopic-microscopic model calibration. These methodologies target different aspects, including individual vehicle behavior, platoon trajectories, and the integration of macroscopic and microscopic traffic flows. Comparative analyses against existing physics-based models demonstrate the exceptional performance of the proposed ES3 model in microscopic traffic flow modeling. Overall, the experimental results indicate its capability to accurately reproduce human drivers’ and autonomous vehicles’ car-following behaviors while elucidating the underlying mechanisms governing the observed macroscopic traffic phenomena.