Stabilization effect of multiple density difference in the lattice hydrodynamic model

In this paper, an extended lattice model is proposed by introducing the multiple density difference effect (MDDE). Stability condition of the new model is obtained through linear stability theory, which shows that considering the MDDE ahead can stabilize traffic flow effectively. The mKdV equation is derived to explore the density waves in the stable and unstable regions, respectively. The kink-antikink solution is obtained from the mKdV equation. Numerical simulation results show that multiple density difference effect (MDDE) can suppress traffic jam considerably, which is in line with the analytical results.