Based on the optimal velocity models, an extended model is proposed, in which multi-veloclty-dllterence aheacl is taken into consideration. The damping effect of the multi-velocity-difference ahead has been investigated by means of analytical and numerical methods. Results indicate that the multi-velocity-difference leads to the enhancement of stability of traffic flow, suppression of the emergence of traffic jamming, and reduction of the energy consumption.
Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries （KdV） and modified Korteweg-de-Vries （mKdV） equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink-antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model -- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.
In this paper, the two-lane traffic are studied by using the lane-changing rules in the car-following models. The simulation show that the frequent lane changing occurs when the lateral distance in car following activities is considered and it gives rise to oscillating waves. In contrast, if the lateral distance is not considered （or considered occasionally）, the lane changing appears infrequently and soliton waves occurs. This implies that the stabilization mechanism no longer functions when the lane changing is permitted. Since the oscillating and soliton waves correspond to the unstable and metastable flow regimes, respectively, our study verifies that a phase transition may occur as a result of the lane changing.
