Analysis of a novel lattice hydrodynamic model considering predictive effect and flow integral

By taking the predictive effect and flow integral into consideration, we propose an improved lattice hydrodynamic model. Firstly, we apply linear stability analysis to acquire the linear stability condition, which can be used to explain the influence of predictive effect and flow integral on traffic flow stability. After that, the modified Korteweg–de Vries (mKdV) equation is derived through the nonlinear theory, which demonstrates that the solution of mKdV equation can describe traffic jams. Besides, the kink–antikink soliton wave is obtained through solving the mKdV equation, which can describe the propagation characteristics of the traffic density waves. Furthermore, we try to explore how predictive effect and flow integral influence the stability of traffic flow through numerical simulations. Finally, we find that the stability of traffic flow can be efficiently improved with the consideration of the two factors by observing and analyzing the numerical results.