An enhanced microscopic car-following model incorporating human driver behavioral dynamics in response to taillight cues

• We introduce a modified microscopic model incorporating driver response to the preceding vehicle’s taillight effect. • The proposed model is analyzed through linear and nonlinear frameworks, both theoretically and mathematically. • This innovative approach significantly suppresses aggressive driver behavior and improves traffic flow stability. • To verify theoretical results, numerical simulations have been conducted. Transportation systems, despite significant advancements in infrastructure and technology, must inevitably consider human driver behavior to ensure safe driving and optimize traffic flow. In this context, we examine the drivers’ mental influence on the taillight effect, incorporating a human response time delay within a single-lane microscopic car-following model. We adopt the full velocity difference (FVD) model and the taillight adaptive model (TAM) as baselines to evaluate our proposed model’s performance. To assess the superiority of our proposed modified taillight adaptive model (MTAM), we perform a combination of theoretical analyses and numerical simulations. To analytically explore the stability of our proposed model, a linear stability analysis has been conducted to derive the neutral stability conditions. In addition, we investigate the complex traffic dynamics in proximity to critical points, and a nonlinear analysis is performed, leading to the derivation of a standard modified Korteweg-de Vries (mKdV) equation with wavy soliton solutions that assist in examining the depth and complexity of traffic behaviors. Finally, numerical simulations and a discussion of the results are carried out on our improved model to illustrate the dynamic evolution of traffic flow. One of our key findings demonstrates that skilled and conscious driving, characterized by minimizing the response time delay to the preceding vehicle’s taillight effect, induces significant traffic stability. Furthermore, reducing the range of the driver’s taillight sensitivity also improves traffic flow performance. Finally, the theoretical and numerical simulation results demonstrate that the MTAM consistently showed better performance than the baseline models.