Nonlinear Analysis For a New Macro Traffic Flow Model Under The Lagrange Coordinate System

In Lagrange coordinates, the macroscopic traffic flow model as a continuum model has a clear correspondence with the microscopic car-following model. In this paper, a new macro continuum model is proposed in Lagrange coordinate based on a car-following model. Using the new model, we carry out the linear stability analysis and investigate nonlinear wave characteristics of macro traffic flow by using traveling wave transformation method. The stability condition of the new model is derived and the stable range of the model is obtained. Then the system behaviors near the neutral stability condition are focused on and the KDV-Burgers equation near the neutral stability condition is deduced by nonlinear analyses. The corresponding solution for traffic density wave is also derived.