Cellular Automaton And Lattice Boltzmann Methods For Traffic Flow Problems

In this thesis.firstlv we introduce the recent studies on traffic flow.which based on the statistical phvsics.such as some theoretical approaches study modelstheir instructive significance and limits in practice.The fundamental principles and characteristics of one-dimension (JD) determined CA model (DCA) and two-dimension determined CA model (BML) are described in details. Secondllv in the 1 D random traffic flow model.the relation function between the correlation and the creation.disappearance.brake probabilities of the vehicles is presented.according to the statistical mechanical approach to the spatial correlation functions.The theoretical results agree with that of the computer simulation.Thirdh.based on the BML model.a main-road traffic flow model with two speeds on two dimensions is designed.This model simulate the traffic situation of one main road and several branches in the cit traffic lights placed on the crossing.vehicles breaking ~vhile running and turning to other direction while jamming.We investigate the ~'e1ocitv and flo~~ of the model when the initial densitvthe brake and turning probabilities.the green to signal rati3.thc number of the branches and the period of the signal are changed.Then the reasons causing all the kinds of phenomena are analvzed.Finallv.we simulate the BML model using the method of lattice boltzmann which ~vas brought out by Liu mu-renand obtain the velocity-density graph similar to the previous result.The upper critical densiw above which there are oniv jamming configurations.and the lo~ver critical density below which there are only moving configurations are the same as before.The boltzmann function which is on the lattices shows the moving and jaxmning transition obviouslv.Thus it proves the possibilit of this method on the traffic research.