Lattice hydrodynamic model for traffic flow on curved road

Considering topography conditions, economic factors and driving safety, in real traffic, a road may be built as curved road. Traffic flow on curved road is different from the one on straight road. And it is worth to investigate the influencing mechanism of traffic flow on curved road. In order to investigate traffic flow on curved road analytically, in this paper, an extended one-dimensional lattice hydrodynamic model for traffic flow on curved road is proposed. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the radian, friction coefficient and curvature radius of curved road. The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived to describe the nonlinear density waves in the stable, metastable and unstable regions, respectively. The simulations are given to verify the analytical results. The results, which obtained from the theoretical analysis and numerical simulations, show that traffic flow may be affected by the angle going into curved road, the increment of angle, friction coefficient and curvature radius of curved road. And the maximal theoretical flux and velocity of traffic flow are influenced by the above factors as well.