The Study On Equilibrium Solution Of Prigogine-Herman Mesoscopic Traffic Flow Model

At present,China is in the period of rapid development of urbanization,large cities and mega cities are transforming and expanding,and the construction of small towns is advancing rapidly.As the artery of the city,traffic not only provides the convenience for people,but also brings many negative effects.Traffic congestion,traffic accidents,environmental pollution and a series of problems have seriously affected people's living conditions.Therefore,it is particularly important to make use of scientific and effective way to ensure that our cities take into account the sustainable development of construction.Traffic flow theory is the theoretical basis for traffic planning and construction,it can reveal the formation mechanism of traffic phenomena,and help us to solve the actual traffic problems.Based on traffic flow theory,this paper focuses on the equilibrium solution of Prigogine-Herman traffic kinetic model,and mainly has following achievements:Firstly,stochastic is created by each drive vehicle unit,derived from the characteristics of the system element itself.Stochastic has negative and destructive effects on traffic flow,which will reduce the average velocity of traffic flow due to it.However,the traditional traffic flow theory considers only the average velocity and density,but the influence of stochastic on traffic flow is neglected.In this paper,we describe the stochastic of traffic state by velocity variance,analyze the stochastic of Prigogine-Herman traffic kinetic model,and define the potential energy of traffic flow,and analyze the relationship between the potential energy and density.Secondly,this paper derives the equilibrium solution of Prigogine-Herman traffic kinetic model by using synergetics.We find that the average velocity of traffic flow is affected by the density and stochastic(velocity variance),and the value has a certain probability.So we present a new flow formula,called the maximum probability method that flow equal to the product of the maximum probability of the average velocity and density.Thirdly,comparing the proposed model with the measured data,it is found that the proposed maximum probability method is better than conventional fluid dynamics method.The research results of this paper have certain value to the understanding of traffic flow process,modeling and the relationship between the basic variables of traffic flow.