Stability analysis of feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory

Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink-antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.