Two Dimensional Continuum Dynamic Traffic Assignment With Land Use Models And Their Numerical Simulations

Dynamic traffic assignment(DTA)is the important theoretical basis of the intelli-gent transportation system for the guidance of traffic flow.According to the abstraction of the urban road network,there are two general approaches for the traffic assignment problem:the continuum modeling approach and the discrete modeling approach.In the continuum modeling approach,the road network is assumed to be a two-dimensional continuum.The characteristic variables are represented by smooth mathematical func-tions,and then differential equations are established to describe the models.Different with the traditional discrete modeling approach,in which the road network is composed of nodes and arcs,continuum modeling approach focuses on the macroscopic character-istics of the transportation system,and it has many advantages in the macro investigation on the transportation system with dense road network.However,the studies for the DTA problem using continuum modeling approach are not enough.Therefore,in this work,we apply the continuum modeling approach to establish and develop the two-dimensional continuum DTA models.Moreover,considering the relationship among transportation system,land use and transportation pollution,we establish the integrated transportation and land use model.The main contents of this dissertation are summarized as follows.1.We extend the two-dimensional continuum predictive dynamic user-optimal(P-DUO)model into a polycentric urban city,and construct the numerical algorith-m based on the unstructured meshes to solve the model.This model is composed of two coupling parts with opposite initial times:conservation law equation and Hamilton-Jacobi equation.In the numerical algorithm,the finite volume method(FVE)is used to solve the conservation law equation,the finite difference method(FEM)is used to solve Hamilton-Jacobi equation,the fast marching method(FM-M)is used to solve Eiknol equation,and the adaptive method of successive average(MSA)is used to solve the fixed-point problem.2.We combine the departure time choice and the PDUO model to establish the two-dimensional continuum dynamic user-optimal model for the simultaneous departure time and route choice(SDTRC-PDUO)problem in a polycentric city.In modeling,we first give the definition of the departure time dynamic user-optimal principle,and then prove that the definition is equivalent to a variational inequality(VI).In the algorithm,we first derive the discrete variational inequality based on triangle meshes,and then apply the GLP projection method to solve it.3.We present a two-dimensional continuum bi-level programming model for the transportation-land use problem.Firstly,considering the relationship between traf-fic demand and housing provision,we establish the integrated housing provision and SDTRC model given total traffic demand and housing provision.As the lower-level subprogram,the transportation system reach the departure time and route choice user equilibrium.In the upper-level subprogram,the total traffic-related emissions(CO2)is minimized by optimizing additional housing allocation.In the numerical algorithm,we use MSA to solve the lower-level subprogram(the inte-grated housing provision and SDTRC model)and Frank-Wolfe method to solve the upper-level subprogram.The major contributions of this dissertation are as follows.1.A two-dimensional continuum predictive continuum dynamic user-optimal model is extended to investigate the traffic equilibrium problem for a polycentric urban city with multiple CBDs.A numerical scheme based on unstructured meshes is constructed to solve the model.2.We firstly consider departure time choice in two-dimensional continuum DTA prob-lem,and present a simultaneous departure time and route choice(SDTRC)model.A numerical method based on unstructured meshes is used to solve the presented model.3.In the continuum modeling framework,we firstly combine the DTA problem with the land use and transportation pollution problem,and present a two-dimensional continuum bi-level programming model for the transportation-land use problem.A numerical algorithm based on unstructured meshes is given to solve the model.In summary,we systemically investigate the two-dimensional continuum DTA models(pure route choice model? simultaneous departure time and route choice(SDTRC)model? integrated housing provision and SDTRC model? transportation-land use model),and construct the numerical algorithms based on unstructured meshes.The works in this dissertation will provide valuable references for theoretical researches and practical applications in the transportation science.