An improved lattice hydrodynamic model accounting for the effect of “backward looking” and flow integral

In order to investigate the effect of “backward looking” and flow integral upon traffic flow, an improved lattice hydrodynamic model has been developed. The stability condition is obtained by the use of linear stability analysis. The result of stability analysis demonstrate that both the “backward looking” and flow integral play an important role in enhancing the stability of traffic flow. The mKdV equation is deduced by using the nonlinear theory, which demonstrates that traffic congestion can be described by the solution of mKdV equation. Numerical simulations are explored to study how “backward looking” and flow integral influence the stability of traffic flow. Numerical results verify that the traffic flow stability can be efficiently improved with the consideration of the above two factors.