Day-to-day Traffic Evolution Model And Dynamic Pricing Under Bi-objective User Equilibrium

At present,the number of vehicles in China is increasing rapidly.Increasing travel demand has put forward higher requirements for the operation efficiency of the transportation system.In academic research of traffic assignment,dynamic traffic assignment models describe the evolution process of traffic flow from a disequilibrium state to an equilibrium state.Studying the dynamic evolution process of traffic is conducive to exploring the internal mechanism of traffic flow evolution,and it is good to induce and control the traffic state so as to improve the efficiency of traffic operation.This paper mainly studies the day-to-day traffic dynamic evolution process.At the same time,based on the day-to-day dynamic route choice behavior of travelers,this paper studies the dynamic tolling scheme to improve the operating efficiency of transportation system.In addition,considering the penetration of emerging technologies into the current transportation market,the dynamic evolution of the traffic flow in a mixed transportation system of traditional gasoline vehicles and electric vehicles is also studied.The specific research content is as follows.Firstly,the day-to-day dynamic evolution model of traffic flow under the bi-objective user equilibrium is studied.Considering the advantages of the bi-objective user equilibrium,a day-today traffic dynamic evolution model based on this equilibrium concept is proposed to characterize the route choice and switch behavior of the traveler day by day.The proposed dynamic evolution model can enable any initial traffic flow pattern eventually to evolve to a bi-objective user equilibrium state.The properties of steady state and convergence of the model were analyzed and proved strictly,and numerical examples were used to verify the model.Then,the dynamic tolling scheme based on the proposed day-to-day dynamic evolution model is studied.Because the bi-objective user equilibrium solution is not unique,its solution set includes some traffic flow patterns with poor system status(larger system travel time).Therefore,this paper designs a dynamic tolling scheme based on the proposed day-to-day dynamic evolution model to improve the system efficiency.This mechanism allows any initial traffic flow pattern to eventually evolve into a smaller equilibrium solution set.This solution set greatly reduces the uncertainty of the traffic flow,and at the same time greatly reduces the system total travel time.The proof of the relevant theoretical properties and numerical example verification of the proposed tolling scheme were presented.Finally,the day-to-day dynamic evolution model of mixed traffic flow,which include gasoline vehicles and electric vehicles under bi-objective user equilibrium is considered.Considering the special characteristics of electric vehicles,the route choice rule for a mixed vehicle transportation system under bi-objective user equilibrium is first defined,and then a day-to-day dynamic evolution model of traffic flow is designed based on this rule.The properties of steady state and the convergence of the model were analyzed and proved strictly.Numerical examples validate the proposed model.