Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow

We analyse the Newell-Whitham-type car-following model described by a differential-difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one. Linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car. From the nonlinear analysis, the propagating kink solution for traffic jams is obtained. The fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation. We find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation.