Two Dimensional Continuum Dynamic Traffic Assignment Models And Their Numerical Simulations

The dynamic traffic assignment (DTA) models together with their solution algo-rithms constitute the theoretical basis of intelligent transportation systems (ITS) for the guidance of traffic flow. These satisfying Wardrop's first or second principles of equi-librium are classified as the traffic equilibrium assignment models, and the others as the traffic non-equilibrium assignment models. By the abstraction of a traffic system, the modeling approaches can be either discrete or continuous. The resultant continuum models concisely depict traffic networks with the complicatedly intersected roads and are mainly used for the initial planning and modeling phase in broad-scale regional traffic studies. The focuses hereby are on the general trend and the distribution pattern of area transportation networks as well as path-choice behavior of any user group at the macroscopic level. Compared with the discrete modeling approach, there are many advantages for the continuum modeling approach. First, it is particularly suited for de-picting a large/dense transportation system. Second, it conveniently depicts a collective path-choice behavior of large amounts of travelers. Third, it provides full information with the quantities of important macroscopic variables (the density, average velocity and flow rate) for the construction and management of transportation networks.For the aforementioned advantages, this dissertation focuses on the DTA mod-els and algorithms based upon the continuum assumption. The contents are arranged to include three major subjects:(1) mathematical modeling; (2) design of numerical schemes; and (3) the simulation applications, which are indicated as follows.In Chapter 2, the continuum single and multiple user-class static traffic equilib-rium assignment models are extended to the dynamic ones which satisfies the dynamic user-optimal principles (i.e. the reactive and predictive user-optimal conditions). Fur-thermore, both one dimensional (1D) isotropic and anisotropic vehicle traffic flow mod-els are extended to deal with the assumed two dimensional (2D) transportation systems. The resultant models substantially enhance the nonlinearity and the dynamic property of traffic flow on road networks and might truly reflect non-equilibrium transportation systems. Theoretical properties including solution existence and linear stability of these models are also investigated.In Chapter 3, some hybrid numerical methods are constructed to solve the devel- oped models. The solution procedure includes three major steps in the following order. First, the unstructured high-resolution finite volume methods are designed for the space discretization of the flow conservation equations. Second, the upwind difference and finite element schemes are used for the space discretization of the user-optimal path choice models, which are essentially the dynamic or static Hamilton-Jacobi equations. Finally, the explicit TVD Runge-Kutta methods are applied for the time discretization of the resultant ordinary differential equations.In Chapters 4-6, the proposed equilibrium and non-equilibrium models and their solution algorithms are applied to study several typical urban DTA problems. Chapter 4 investigates the single user-class predictive dynamic traffic equilibrium assignment pat-tern of traffic flow on a road network with a single absorption point (e.g., a central busi-ness district); Chapter 5 deals with the multiple user-class reactive dynamic traffic equi-librium assignment pattern of traffic flow on a dense network (e.g., bi-direction pedes-trian flow moving in a railway platform with two pairs of entrances and exits); Chapter 6 applies the non-equilibrium isotropic model to simulate the single user-class reactive dynamic traffic non-equilibrium assignment pattern of unidirectional pedestrian flow passing a walking facility with an obstruction. All these numerical simulations indicate that macroscopic traffic characteristics of dynamic traffic flow on networks, the forma-tion and dissipation process of traffic congestion, and travelers' path-choice behaviors can be predicted in short term by the proposed continuum DTA models. Both qualita-tive and quantitative results will provide useful information for planning and design of an urban transportation system as well as for traffic control and management.In summary, this dissertation systematically studies the DTA problem for a large/dense transportation system through the development of 2D continuum models and the construction of hybrid numerical schemes. The contents together with the sim-ulation results as a whole will surely provide new references for theoretical researches and practical applications in the transportation science.