Modeling And Simulation Of Some Traffic Problems,and Related Theoretical Analysis

This dissertation is concerned with the modeling of the integrated landuse,transportation and environment problems by continuum modeling approach,numerical simulation and related theoretical analysis.The dissertation is mainly divided into the following four parts:In the first part,we model and simulate the dispersion of vehicle exhaust in a hypothetical city with a single central business district(CBD)in a complete day,deriving an average daily pollutant concentration,then use the distribution of wind direction over a year,to compute the distribution of average pollutant concentration in the city.All vehicles are assumed to be continuously distributed over the whole city,and the road network is relatively dense and can be approximated as a continuum.The reactive dynamic user-optimal model is used to describe the traffic flow that satisfies the reactive dynamic user equilibrium principle,and the pollution dispersion model is governed by the advection-diffusion equation.The complete model is composed of a coupled system of a conservation law,an eikonal equation and an advection-diffusion equation.The problem is solved by the efficient fifth-order weighted essentially non-oscillatory scheme for the conservation equation and the advection-diffusion equation,and the fast sweeping method for the eikonal equation with third order total variation diminishing(TVD)Runge-Kutta time discretization.The numerical results show a reasonable temporal and spatial distribution of vehicle density and pollution concentration.In the second part,we proposes a predictive continuum dynamic user-optimal model with combined choice of housing location,destination,route,and departure time.A traveler’s choice of housing location is modeled by a logit-type demand distribution function based on air quality,housing rent,and perceived travel costs.Air quality,or air pollutants,within the modeling region are governed by the vehicle-emission model and the advection-diffusion equation for dispersion.In this chapter,the housinglocation problem is formulated as a fixed-point problem,and the predictive continuum dynamic user-optimal model with departure-time consideration is formulated as a variational inequality problem.The Lax-Friedrichs scheme,the fast-sweeping method,the Goldstein-Levitin-Polyak projection algorithm,and selfadaptive successive averages are adopted to discretize and solve these problems.A numerical example is given to demonstrate the characteristics of the proposed housing-location choice problem with consideration of air quality and to demonstrate the effectiveness of the solution algorithms.In the third part,we considered the housing allocation and traffic emission problem in an urban city with a single central business district(CBD)by using a bilevel dynamic continuum transportation model.In the lower-level subprogram,a predictive dynamic continuum user-optimal(PDUO-C)model with a combined departure time and route choice was used to study the city traffic flow under a fixed housing allocation.Using the upper-level subprogram,the health cost was defined and minimized to identify the optimal allocation of additional housing units.Here a simulated annealing algorithm was used to solve the housing allocation problem in the upper-level subprogram.Additionally,a numerical experiment that demonstrates the effectiveness and efficiency of the model and the numerical algorithms is presented.In the fourth part,we addresses the existence and uniqueness of solutions to the Hoogendoorn-Bovy(HB)pedestrian flow model,which can also be generalized to to study user-optimal dynamic traffic assignment problems in continuous space and time.The HB model consists of a forward conservation law(CL)equation that governs the density and a backward Hamilton-Jacobi-Bellman(HJB)equation that contains a maximum admissible speed constraint(MASC),in which the flow direction is determined by the path-choice strategy.The existence and uniqueness are significantly more difficult to analyze when the HJB equation contains the MASC;however,we prove that the HB model can be formulated as a forward CL equation and backward Hamilton-Jacobi(HJ)equation in which the MASC is non-binding if suitable model parameters are chosen.This model is formulated as a fixed-point problem upon the simultaneous satisfaction of both equations.To verify the existence and uniqueness results,we first show the existence and uniqueness of the solutions to the CL and HJ equations,and then demonstrate that the coupled HB model is well-posed and has a unique solution.A numerical example is presented to demonstrate the properties of the HB model.