An extended multi-anticipative delay model of traffic flow

• An extended multi-anticipative delay model of traffic flow is developed.
• The effects of multiple velocity differences and the reaction-time delay on the stability of traffic flow is investigated.
• Results demonstrate that multiple velocity differences consideration lead to enhance the stability of traffic flow.
• The stability is strengthened with decreasing the reaction-time delay of drivers.

An extended multi-anticipative delay model is proposed by introducing multiple velocity differences and incorporating the reaction-time delay of drivers. The stability condition of the new model is obtained by applying the linear stability theory, and the modified Korteweg–de Vries (mKdV) equation is derived by the use of the nonlinear analysis method. The analytical and numerical results show that both the reaction-time delay of drivers and the information of multiple velocity differences have an important influence on the stability of the model, and that the stabilization of traffic flow is enhanced by appending the velocity difference information of multiple vehicles ahead or by decreasing the delay time.