Curved Road Traffic Dynamics: A Lattice Model Integrating Visibility Effects and Predictive Driving Behavior

Abstract This study presents a comprehensive lattice model specifically designed to enhance visibility on curved roads, thereby improving the ability of drivers to anticipate and respond to traffic conditions. The model demonstrates that the integration of strategic infrastructure improvements and advanced technological solutions significantly enhances drivers' predictive accuracy. To analyze traffic stability, the reduced perturbation method is applied, enabling the derivation of the density wave equation which provides a framework for understanding how traffic congestion propagates near critical thresholds. The findings indicate that traffic flow stability on curved roads is positively correlated with increased driver prediction capabilities and negatively correlated with reduced visibility. Furthermore, nonlinear analysis technique is utilized to derive the modified Korteweg–de-Vries (mKdV) equation, which effectively characterizes the evolution of traffic density waves in congested or jammed traffic regions. The overall effectiveness of the proposed vehicle driving systems' model has been validated through extensive numerical simulations, particularly under conditions of high traffic density, confirming its potential applicability for real-world traffic management on curved roadways.