Behavioral dynamics of a modified car-following model integrating multiple delays and driver reaction to the preceding vehicle taillight signals

Within the Intelligent Transportation System (ITS) applications, numerous studies have been conducted using various analytical frameworks to examine traffic flow dynamics. By adopting these technologies, drivers can achieve intelligent driving by receiving enhanced traffic information. Our proposed modified car-following model incorporates several factors, such as multiple time delays and human reaction to the preceding vehicle taillight signals. This study aims to present an improved traffic model that incorporates three crucial features, accounting for multiple time delays in sensing both headway and velocity information and human reaction delay to the preceding vehicle taillight signals to optimize traffic flow and diminish traffic instability, building upon the Taillight Adaptive Model (TAM) and the Full Velocity Difference (FVD) model. To investigate the influence of these multiple delays, we perform linear analysis, nonlinear analysis, and numerical simulations of our proposed model. Neutral stability conditions have been derived using linear stability analysis theory, demonstrating stable, metastable, and unstable regions. Employing nonlinear theory, three distinct nonlinear wave equations are obtained, namely the Burgers’ equation, Korteweg–de Vries (KdV) equation, and modified Korteweg–de Vries (mKdV) equation, which characterize soliton waves and kink-antikink wave solutions in the stable, metastable, and unstable regions, respectively. Finally, comprehensive numerical simulations have been conducted to validate our proposed model and depict the dynamic evolution of traffic flow under various parameter configurations. The obtained outcomes demonstrate that reducing distance-sensing delay, along with decreasing human reaction delay to the preceding vehicle’s taillight signals, substantially suppresses traffic congestion, while the velocity-sensing delay exhibits an opposite effect. The analytical and numerical simulation results demonstrate strong mutual consistency, validating the theoretical framework.