Theoretical Analysis of a Modified Continuum Model

Based on the optimal velocity (OV) model, a new car-following model for traffic flow with the consideration of the driver's forecast effect (DFE) was proposed by Tang et al., which can be used to describe some complex traffic phenomena better. Using an asymptotic approximation between the headway and density, we obtain a new macro continuum version of the car-following model with the DFE. The linear stability theory is applied to derive the neutral stability condition. The Korteweg–de Vries equation near the neutral stability line is given by nonlinear analysis and the corresponding solution for the traffic density wave is derived.