Stability Analysis of the New Traffic Flow Lattice Model considering Taillight Effect and Speed Deviation

Abstract

A new macroscopic traffic flow lattice model is established which considered the taillight effect and velocity deviation. By combining the concept of critical density, the critical condition of taillight triggering is established. The situation of taillight appearing is fully considered, and the influence of taillight effect is analyzed. Through the stability analysis of the model, the stability conditions of the model are obtained. By nonlinear analysis, the mKdV equation is derived which can describe the evolution mechanism of the density wave. From the phase diagram, we can find that the two factors have a positive impact on the stability of traffic flow. Finally, spatiotemporal evolution of the density wave and cross-section view of the density wave are obtained by numerical simulation to verify the theoretical derivation of this paper. The simulation results show that the stability of traffic flow can be improved by considering taillight effect and speed deviation. In addition, by comparing the time-space evolution maps of different parameter values, it can be found that the stability of traffic flow considering the taillight effect and speed deviation is better than that considering one factor alone. However, the stability of traffic flow will be negatively affected by low speed estimate and high critical density.