Analytical studies on a new lattice hydrodynamic traffic flow model with consideration of traffic current cooperation among three consecutive sites

In this paper, the original lattice hydrodynamic model of traffic flow is extended to take into account the traffic current cooperation among three consecutive sites. The basic idea of the new consideration is that the cooperative traffic current of the considered site is determined by the traffic currents of the site itself, the immediately preceding site and the immediately following one. The stability criterion of the extended model is obtained by applying the linear stability analysis. The result reveals the traffic current cooperation of the immediately preceding site is positive correlation with the stability of traffic system, while negative correlation is found between the traffic stability and the traffic current cooperation of the nearest follow site. To describe the phase transition, the modified KdV equation near the critical point is derived by using the reductive perturbation method, with obtaining the dependence of the propagation kink solution for traffic jams on the traffic current cooperation among three consecutive sites. The direct numerical are conducted to verify the results of theoretical analysis, and explore the effects of the traffic current cooperation on the traffic flux of the vehicle flow system.