Analysis Of The Nonlinear Density Wave In Macro Trafc Fow Model

This paper aims to study nonlinear density wave in macroscopic model of trafc fow.Based on the existing microscopic car-following model, and considering the relationship be-tween micro and macro variables, we propose an improved model. The reasonable analysisand computer simulation are used to the new model. The main research is as follows:I. The KdV-Burgers equation in an improved speed gradient model.Based on the full velocity model, we get a new speed gradient model by adopting themacro-micro linkage and Taylor expansion to second order, and keep the anisotropic charac-teristics. Through linear analysis we obtain the neutral stability curve. The KdV-Burgersequation is derived to describe the nonlinear density wave of trafc fow near the neutralstability line, which is hardly found in previous models. We make numerical simulation andgive the graph of density wave evolution under diferent initial density, which is consistentwith theoretical results.II. Continuum model with consideration of driver’s forecast efect.In real trafc, driver’s behavior has great efect on trafc fow. Considering the efect ofdriver’s prediction, Zheng et al. put forward a new efective model, we get the correspondingmacro model by adopting the more precisely spacing and density relation. We derive KdVequation through theoretical analysis and carry out numerical simulation to the model. Then,we propose a new two velocity diference car-following considering the driver’s predictionefect. We also make some correlation analysis to the new model. The KdV-Burgers equationis obtained, and get a conclusion that appropriate prediction time can improve the stabilityof trafc fow.III. Two lane hydrodynamic model considering driver’s prediction efect.This chapter using the idea of Nagatani, we get the corresponding two lane hydrodynam-ic model with consideration of driver’s prediction efect through establishing the relationshipbetween diference equation and diferential equation. Until now, a large number of nonlinearanalysis is used to the single-lane trafc fow, but rarely to the two-lane continuum model.The majority work is numerical simulation. Luckily, we not only make linear analysis to thenew model, but also derive the KdV-Burgers equation of the two lane hydrodynamic modelthrough nonlinear analysis.