The Application Of The ASEP Model In Traffic Flow

Problems like financial losses,environmental pollution and traffic accidents which caused by traffic jam have attracted attentions of a number of scholars.For avoiding traffic congestion,how to relieve the traffic pressure has been a difficult question to be solved as soon as possible.As a kind of basic theory in studying traffic jam mechanism,traffic flow theory was put forward and with rapid development in these decades,hundreds of traffic flow models have been proposed so far.By continuous improvement and perfection,here asymmetric simple exclusion process(ASEP)with its easy understanding,high computing accuracy and liable expansion stands out of numerous micro-traffic models.In addition,properties that some complex phenomenon(spontaneous breaking of symmetry,phase transition caused by boundary conditions,shock formation,etc.)happened in non-equilibrium system can be simulated by this process make it being one of the most important models in studying traffic flow theory.Nowadays,this model is also widely used in physics,chemistry and biology field by being a necessary method in researching non-equilibrium phenomenon.Three kinds of ASEP models which started with real roads by using mean-field theory as analytic method and Monte Carlo computer simulation have been studied in this article.In chapter three,the ASEP model based on two-lane coupling road with unequal injection rates and only one direction lane-changing has been considered,meanwhile,different hoping rates is thought about as a variation in this model.By using random update as the update rule to analyze the system,the results we get show that the phase diagram is related to the hopping rates of these two lanes,but has no business with lane-changing rate.If the hopping rates of two lanes are the same,the phase diagram contains six steady states;when they are not equal,there comes the seventh steady state(MC,MC).The results of computer simulation and theoretical analysis agree well.In chapter four,the ASEP model with a single defect site on left or right boundary,whose prototype is the road of speed limited at entrance and exit,has been researched with using random update as motion rule,to see how the single site with different hopping rate affects the system.The results indicate that the line 2p=q2 is the boundary of whether the steady state MC exists in the phase diagram.If the relationship of p and q satisfies 2p?q2,there is no MC phase in system.While,if it satisfies 2p>q2,the phase diagrams of these two models are similar to the normal asymmetric exclusion process.When phases of LD,HD and MC all exist in phase diagram,reducing the value of p/q makes HD phase shrink in entrance speed limiting model and expand in exit speed limiting model.The consequences of simulation and calculation are in agreement.In fifth chapter,a TASEP model with a roundabout by using parallel update rule has been built,in which,two special sites are set far away from boundaries for getting particles in and out with rates p and q.After analyzing this model,the consequences explain that the phase diagram has seven steady states and they will expand or shrink if the value of p or q changes.However,no states will disappear in this system.The outcomes of mean-field theory analysis and computer simulation are basically similar.