Self-Anticipation and Current Difference Effect in Lattice Model under Lane-Changing Behavior

Objectives: To develop a two-lane “lattice hydrodynamic model” incorporating “optimal current difference” and “self-anticipation” to improve traffic flow stability and reduce congestion. Methods: A two-lane lattice model is introduced, incorporating both “optimal current difference and self-anticipation effect”. Linear stability analysis alongside the reductive perturbation technique for deriving mKdV equations and nonlinear calculations are utilized to evaluate the model's impact on traffic stability and congestion, with theoretical results further validated through numerical simulations under periodic boundary conditions. Findings: The linear stability analysis reveals that the “self-anticipation” term significantly expands the stable region in the phase diagram compared to Peng's lattice model. The derived modified Korteweg-de Vries (mKdV) equation highlights heavy traffic near the critical point, indicating areas where congestion is most severe. Nonlinear calculations further demonstrate that incorporating both anticipation time and lane-changing behavior coefficient effectively reduces congestion. This combined approach smooths out traffic flow, especially in areas near the critical point of congestion. The findings suggest that drivers' self-anticipation has a differential effect that directly mitigates vehicular congestion, as drivers are better able to adjust behavior based on traffic conditions. Additionally, numerical simulations conducted with periodic boundary conditions confirm the effectiveness of these theoretical solutions in practice, reinforcing the model's applicability to real-world traffic conditions. Novelty: The model integrates “self-anticipation and optimal current difference”, expanding vehicles' stability and mitigating congestion more effectively than existing models. Keywords: Two-lane lattice model, Traffic flow, Anticipation, Current difference, Simulation