Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg-de Vries (KdV) equation near the neutral stability line and the modified Korteweg-de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.