A new heterogeneous traffic flow model based on lateral distance headway

Based on a density gradient model proposed recently by Imran and Khan, a new heterogeneous traffic flow model considering time and lateral distance is proposed. The type and stability of the equilibrium solution of the model are discussed by using the differential equation theory, and the global distribution structure of the trajectory in the phase plane is analyzed. In addition, the density wave stability conditions and saddle-node bifurcation conditions of the model are studied, and the solitary wave solutions of the KdV equation in the metastable region are derived by using the reduced perturbation method. The numerical results show that the new model cannot only reproduce the spatiotemporal oscillation phenomenon when walking and stopping, but also describe the sudden change behavior of traffic near the critical point of saddle-node bifurcation. It is shown that the model can reproduce some complex traffic phenomena qualitatively.