A lattice traffic model with consideration of preceding mixture traffic information

In this paper, the lattice model is presented, incorporating not only site information about preceding cars but also relative currents in front. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution and find that the improvement in the stability of traffic flow is obtained by taking into account preceding mixture traffic information. Direct simulations also confirm that the traffic jam can be suppressed efficiently by considering the relative currents ahead, just like incorporating site information in front. Moreover, from the nonlinear analysis of the extended models, the preceding mixture traffic information dependence of the propagating kink solutions for traffic jams is obtained by deriving the modified KdV equation near the critical point using the reductive perturbation method.