Nonlinear Analysis of a Dynamical Model with Next-nearest-neighbor Interaction for Traffic

We analyze a dynamical model of car-following model analytically and numerically, which is a continuation of our previous research on traffic flow in stable region. Linear stability analysis shows that our model is stabilized for larger delay time by taking into account the relative velocity of the immediately preceding car. Moreover, the Burgers equation is derived for the density wave in stable region of traffic flow from nonlinear analysis, the result of direct simulation show that the triangular shock wave appears as the density wave at later stage in stable region.