Anisotropy and Stabilization of Traffic Flow in Extended Cooperative Driving Lattice Hydrodynamic Models Based on Backward-Looking Effect

Abstract

Two extended cooperative driving lattice hydrodynamic models are proposed by considering the backward looking effect in traffic flow. The stability conditions for the two models are investigated with the linear stability theory and it is found that new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.