About The Traffic Flow Model In A Number Of Issues

Traffic has become a world-wide problem. Traffic jam and traffic pollution result into great social pressure and economic loss. How to utilize traffic resources efficiently, improve the relation between traffic supply and demand, and direct traffic building and operation with traffic science become urgent issues. Traffic is a multi-body system with complex interaction in human society, which includes vehicle, traffic environment and human being, and has inner relations with physics, mechanics, mathematics, information science, traffic engineering, etc. Study on traffic flow is not only profound scientifically significant, but also valuable for engineering application.The object of traffic flow research is to build traffic flow model which can reflect the general properties of the real traffic according to traffic phenomena and empirical data in order to disclose the basic laws of traffic flow. According to theoretical basis and research methods, the traffic flow models can be classified into macroscopic, meso-scopic and microscopic ones. Macroscopic fluid mechanics models, mesoscopic gas-kinetic-based models, microscopic car-following and cellular automata models have the same research object and can mutually reinforce and co-develop. The fluid mechanics model has special advantages in disclosing nonlinear phenomena and macroscopic characteristics of traffic flow. This thesis continues to do research on macroscopic traffic flow model — pipe flow model and velocity-density dependence with the nonlinear stability analysis, metastability and two dimensional region of congested traffic. The dimensional analysis is an important clue. Most numerical simulations and mathematic analysis in this thesis are dimensionless. the similarity of model and the determination of parameters' range and dependence will also use dimensional analysis theory . The contents of the paper are as follows.Different traffic flow models have similar functions in explaining traffic phenomena, and parameters in different models can be analogized. Therefore we introduce the dimensional analysis into traffic flow and do research on model parameters. Some dependences can be found in the dimensionless parameters: the relaxation time is inversely proportional to equivalent sound velocity; The relaxation time of high-speed highway is larger than that of slow-speed highway; The equivalent sound velocity of high-speed highway is smaller than that of slow-speed highway. The numerical sim-ulation of a traffic phenomenon can determine a parameter's range in the light of real traffic. This method and similarity theory are used to do research on traffic state parameter in the pipe flow model.We summarize some usual isotropic and anisotropic traffic flow models, and then get a general form of one-order two-equation traffic flow model. We have done linear and nonlinear analysis on this general form and find that the general nonlinear stability criteria given by parameters and the general linear stability criteria are consistent in judging stability. Especially, the stability criteria of the PW-like model and the Zhang-like model is linearly same and nonlinear similar, and both of them are dependent on initial conditions, equivalent sound velocity and equilibrium function, which is a theoretical warranty that stability analysis can be used to velocity-density dependence. The parameters of nonlinear stability criteria can qualitatively describe the trend of traffic flow perturbation and change of traffic flow states, whose stability varies with parameters' values. With stability-criterion parameters, we examine the critical states and the effect on traffic perturbations that one characteristic velocity is larger than average flow velocity in anisotropic traffic flow models, and especially find the downstream-moving perturbations will decay quickly in pipe flow model, which can still be used for the simulation of traffic perturbations. The general rules of stable and unstable propagations are demonstrated by an example.We improve the pipe flow model, determine the value of the traffic state parameter according to similarity theory of dimension analysis. We use pipe flow model to simulate narrow, wide and dipole clusters with right difference scheme, and the stable and the metastable cluster structures can be distinguished in fundamental diagram. The numerical simulations show some new characteristics of cluster. The "flow-density velocity" and traffic state parameter empirical formulae are used to do research on cluster and wave velocity, examine the congested characteristics of cluster, and propose a range of wave velocity in congested traffic regime. We take mathematic analysis on characteristic parameters of cluster in the general form of traffic flow model, and get the velocity formula of stationary moving cluster, which shows that the cluster's velocity is different from characteristic velocity.We notice that some flow-density curves yield wave velocities which are not consistent with empirical values. Using two-dimensional region of congested traffic,...