A New Lattice Hydrodynamic Model for Traffic Flow on Curved Road

Abstract

Due to topographical features, economic considerations, and driving safety, roads in actual traffic scenarios are often constructed with curves. Therefore, it is important to explore how traffic flow is influenced by curved roads. To analytically examine traffic behavior on such roads, this study introduces an extended lattice hydrodynamic model  for curved road conditions. Using linear stability analysis, the conditions for traffic stability are derived. The findings indicate that traffic stability is influenced by factors such as the curvature of road, friction coefficient and turning angle of the road. Furthermore, the Korteweg–de Vries (KdV) equation, and the modified KdV equation are obtained to represent nonlinear density waves in stable, metastable, and unstable traffic regimes, respectively. Numerical simulations are conducted to support the analytical findings. Both theoretical analysis and simulation results demonstrate that traffic flow is significantly affected by the curvature and the curve angle of the road. Additionally, these factors also have an impact on the maximum theoretical traffic flux and vehicle speed.