Analysis of a new car-following model with a consideration of multi-interaction of preceding vehicles

A new car-following model was developed to describe the motion of the dynamical traffic flow with a synthesized optimal velocity function which depends on not only headway of the immediately preceding vehicle but also the interactions of an arbitrary number of preceding vehicles. We analyzed the linear stability of this model by introducing a small disturbance into the homogeneous traffic flow on a single circular lane. The stability condition shows the larger delay time of response than previous models. The modified Korteweg-de Vries (mKdV) equation was derived by performing the nonlinear analysis near the critical point and the kink-antikink soliton solution was obtained also. The traffic jams can be suppressed by introducing the more front interactions. The results of the numerical simulation show the validity and the correctness of the new model.