A Continuum Modeling Approach to Traffic Equilibrium Problems

This dissertation, "A Continuum Modeling Approach to Traffic Equilibrium Problems" by Hung-wai, Ho, 何鴻威, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: ABSTRACT for the thesis entitled A CONTINUUM MODELING APPROACH TO TRAFFIC EQUILIBRIUM PROBLEMS submitted by HO Hung Wai for the Degree of Doctor of Philosophy at the University of Hong Kong in August 2005 In modeling traffic equilibrium problems for a transportation system, two different approaches, the discrete and the continuum modeling approach, are commonly adopted. The continuum modeling approach is mainly used for initial planning and macroscopic studies, and depending on the configuration of the modeling region can be classified into models of specific or arbitrary region configuration. This thesis aims to develop the continuum modeling approach with arbitrary region configuration for application in more realistic and complicated situations. The thesis first focuses on applying the continuum modeling approach to the airport competition problem of domestic and international flights within the Pearl River Delta. In this model, air passengers make their choice of airport based on the air ticket price and the transportation cost, which depends on their geographical location. The current situation and four alternative policy scenarios are considered, and reasonable results are found and interpreted. The continuum modeling approach is then applied to formulate a cordon-base congestion pricing problem. This problem is first formulated as a minimization problem, and the first-best solution, in which the net economic benefit is maximized, is found. For a more practical implementation, the toll contours in the first-best solution are selected as toll charging cordons, and a second-best solution is found by further optimizing the toll that is charged in these cordons. In a more theoretical development of the continuum modeling approach, the thesis introduces the idea of multiple user classes into continuum models for the traffic equilibrium problem. System users with different perceptions of transportation and facility costs are considered in this model, and a logit-type demand distribution function is specified to model the probabilistic choice of destinations among multi- class users. Two different optimization approaches are developed to solve the minimization program formulated for this multiple user class problem. The thesis also extends the continuum modeling approach to include housing- related parameters as one of the control variables. A bi-level model is formulated to find the optimal housing provision pattern. In the lower-level model, housing rent is included in the utility function in the traffic equilibrium problem, which affects the allocation of demand. In the upper-level model, the total utility of users is optimized with respect to the housing provision pattern. An effective solution algorithm and numerical example are presented for this housing-related continuum model. DOI: 10.5353/th_b3193826 Subjects: Traffic estimation - Mathematical models