An Evolving Traffic Network Model And Analysis About Paradox,Robustness

With the economic developing and living standards of people improving, the number of private cars is increasing year by year, the problem about the traffic congestion is getting more and more serious, the reasonable transportation planning is urgent. In the context, the appearance of ’four-stage’ method lays the foundation for the development of transportation planning, thereafter, many models are proposed successively. From the summary from the research of the last few decades, the research methods of transportation planning are mainly divided into two categories:macro methods and microscopic methods. The macro methods mainly include ’four-stage’ method, LWR(Lighthill-Whitham-Richards) model and so on; the microscopic methods include cellular automata model, car-following model, etc. In this paper, we propose an evolving traffic network model based on the theory of cellular automata model and double-horizon model in microcosmic, investigate the paradox and robustness of the network under different assignments macroscopically. The main research results are as follows:In chapter Ⅱ, we propose an evolving traffic network model, in which, the influence of next-nearest neighbor is considered. Specifically, the degree distribution of network is described under the influence of the neighbor and the next-nearest neighbor; the influence of some parameters to the distribution of the network is discussed, such as the density, the maximum velocity, the random probability, the number of cells; some characteristics of hubs are given. In the model, the changes of the degree distribution of the network show the congestion state of the traffic flow on roads. Considering the influence of the next-nearest neighbor on the basis of the existing models is an effective complement to the traffic network model.In chapter Ⅲ, we discuss Braess’ paradox and robustness under the user equilibrium and the random user equilibrium. In the process of the user equilibrium, considering the influence of both the link flow and other links flow to the link congestion, we discuss the specific range that the paradox occurs and the influence of the adding link to the occurrence of the paradox, the effect of the adding link under the system optimal and the difference of the total congestion under different equilibrium states, the robustness of the components of the traffic network in four ranges. Under the random user equilibrium, we analyzed the specific range that the paradox occurs, the influence of the adding link to the occurrence probability of the paradox and the robustness of the components of the traffic network in five ranges.In chapter IV, we build a new dynamic traffic network model based on the variational inequality, in which, the link congestion at time t is related to the link flow and other links flow at time t. Under the assumption, we propose the definition of the dynamic equilibrium state and prove the equivalence between the dynamic equilibrium state and the variational inequality. On this basis, we discuss the paradox and influence of other links to the paradox of the dynamic traffic network, the effect of the adding link under the dynamic system optimal and the difference of the total congestion under different dynamic equilibrium states.