Dynamical model of traffic congestion with the consideration of the next-nearest-neighbor interaction

By introducing the velocity difference between the preceding car and the car before the preceding one into the optimal velocity model (OVM), we present an extended dynamical model which takes into account the next-nearest neighbor interaction. The stability condition of this model is derived by considering a small perturbation around the uniform flow solution with finding that traffic congestion is suppressed efficiently by incorporating the effect of new consideration. Then we investigate the property of the model using numerical methods. The results indicate that the next-nearest-neighbor interaction has important impacts on the coexisting flow, the relation between flow and density, and the propagation speed of small disturbance (PSSD). In addition, we have a try to further enhance the stability of traffic flow by introducing the relative velocity of an arbitrary number of cars in front, but the analysis of linear stability shows it is poor for our purpose.