Nonlinear analysis of an extended traffic flow model in ITS environment

An extended traffic flow model is proposed by introducing the relative velocity of arbitrary number of cars that precede and that follow into the Newell–Whitham-type car-following model. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability of traffic flow is improved by taking into account the relative velocity of cars ahead and backward. By applying the nonlinear analysis the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point. The kink–antikink soliton, the solution of the mKdV equation, is obtained to describe the traffic jams. From the numerical simulation, it is shown that the traffic jams are suppressed efficiently by taking into account the relative velocity of cars ahead and backward. The analytical results are consistent with the simulation one.