Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction

The car-following model of traffic is extended to take into account the car interaction before the next car ahead (the next-nearest-neighbor interaction). The traffic behavior of the extended car-following model is investigated numerically and analytically. It is shown that the next-nearest-neighbor interaction stabilizes the traffic flow. The jamming transition between the freely moving and jammed phases occurs at a higher density than the threshold of the original car-following model. By increasing the maximal velocity, the traffic current is enhanced without jam by the stabilization effect. The jamming transition is analyzed with the use of the linear stability and nonlinear perturbation methods. The traffic jam is described by the kink solution of the modified Korteweg--de Vries equation. The theoretical coexisting curve is in good agreement with the simulation result.