KdV-Burgers equation in the modified continuum model considering the "backward looking" effect

Considering the backward looking effect, a modified continuum model is put forward. The stability criterion of this continuum model is deduced by performing linear stability analysis. The theoretical result demonstrates that the traffic flow is stabilized considering backward looking effect. The KdV-Burgers equation is obtained through perturbed nonlinear analysis, which could show the propagating process of density wave. Numerical simulation is carried out to explores how backward looking affected each car's velocity, density and energy consumption. Numerical results demonstrate that backward looking effect has significant impact on traffic dynamic characteristic. In addition, the energy consumptions of this modified continuum model are also studied. Numerical simulation results indicate that the effect of backward looking will suppress the traffic jam and decrease cars' energy consumptions during the whole evolution of small perturbation.