Nonlinear analysis for a modified continuum model considering driver's memory and backward looking effect

Account for the “integral form of optimal velocity changes with memory” and “backward looking” effect, an extended car-following model is proposed in this paper. Through the relation between macro and micro variables, the extended car-following is transformed to a new continuum model. According to the linear stability theory, the linear stability's condition of the presented model is obtained. The modified KdV-Burgers equation is established through non-linear analysis to describe the spreading behavior of the traffic density wave near the neutral stability line. The numerical simulation results show that the “backward looking” effect can improve the traffic flow's stability and the “integral form of optimal velocity changes with memory” can relieve the traffic congestion.