Theoretical analysis of the density wave in a new continuum model and numerical simulation

Considered the effect of traffic anticipation in the real world, a new anticipation driving car following model (AD-CF) was proposed by Zheng et al. Based on AD-CF model, adopted an asymptotic approximation between the headway and density, a new continuum model is presented in this paper. The neutral stability condition is obtained by applying the linear stability theory. Additionally, the Korteweg–de Vries (KdV) equation is derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the neutral stability line. The numerical simulation and the analytical results show that the new continuum model is capable of explaining some particular traffic phenomena.