The Random Dynamics Models For Two-Lane Traffic Flow

In this paper, we mainly study the accelerative process which the vehicle run in the two-lane, then put forward the mathematical model which the moving process of the vehicle is accelerated by the front one. Thus we obtain a two-lane stochastic model of the following form:where 1-g is the proportion that corresponds to the optimization speed accelerated vehicle,1-g is the probability that corresponds to the vehicle which is changing its optimization of acceleration,g is the proportion that corresponds to the proportion of relative speed in the acceleration of the vehicle, and g1 is the probability that corresponds to the traffic in the same way to optimize of acceleration of vehicles.In the third chapter of this article is based on the following model which is put forward by Xue Yu. We discuss the above model by using mathematical theory, and then get a new partial differential equation model which can describe two-lane traffic running process. This model overcomes the issue of the mufti-lane vehicle changing line that does not consider in some mathematical model. In the second part of the third chapter, we study its well-posed property. We mainly use the power series to get solution of dynamic equation, then we study the basic properties of the solution, including uniqueness, convergence and so on.Many dynamic model lack of the numerical simulation of theory and measure. In the fourth chapter of this article we will do two kinds of numerical simulation.One is the traffic flow measuring of urban road with the established dynamic model,and the other is using highway measured data with the established dynamic model. We prove respectively that city crowed roads and expressways meet the established dynamic model.