Analysis of a novel two-lane lattice model on a gradient road with the consideration of relative current

• A novel lattice model for traffic theory is proposed. Numerical simulations are carried out. The Burgers, KdV, and mKdV equations are obtained.

In this paper, a novel hydrodynamic lattice model is proposed by considering of relative current for two-lane gradient road system. The stability condition is obtained by using linear stability theory and shown that the stability of traffic flow varies with three parameters, that is, the slope, the sensitivity of response to the relative current and the rate of lane changing. The stable region increases with the increasing of one of them when another two parameters are constant. By using nonlinear analysis, the Burgers, Korteweg–de Vries, and modified Korteweg–de Vries equations are derived to describe the phase transition of traffic flow. Their solutions present the density wave as the triangular shock wave, soliton wave, and kink–antikink wave in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. To verify the theoretical results, a series of numerical simulations are carried out. The numerical results are consistent with the analytical results. To check the novel model, calibration are taken based on the empirical traffic flow data. The theoretical results and numerical results show that the traffic flow on the gradient road becomes more stable and the traffic congestion can be efficiently suppressed by considering the relative current and lane changing, and the empirical analysis shows that the novel lattice model is reasonable.