An analytical approach to sustainable transportation network design

This dissertation emphasizes the modeling and computation of multi-agent, dynamic, interdependent, complex and competitive transportation systems, by invoking mathematically canonical and tractable forms. Applications of such work focuses on the design and management of a transportation network, which include not only problems of adding/removing capacity by changing nodes and arc sets, but also the determination of piecewise smooth decision variables like prices, tolls, traffic signals, information accessibility, and other control variables associated with Stackelberg mechanisms and so-called second-best strategies.;The primary modeling paradigms employed by this dissertation are differential Nash-like games and differential Stackelberg games that are constrained by systems of (partial) differential algebraic equations. Such modeling paradigms capture several key elements of modern traffic networks including travel choices, demand evolution, vehicular flow propagation, as well as their economic, social and environmental impacts. The model of simultaneous route-and-departure choice dynamic network user equilibrium developed in the early 1990s has been extended in this dissertation to incorporate elastic travel demands and bounded rationality. The invocation of infinite-dimensional variational inequality and differential variational inequality formulations of Nash-like differential game allows existence, uniqueness, computability, stability and other qualitative properties of these models to be addressed and answered.;A critical component of the Nash-like network congestion game is the so-called dynamic network loading (DNL) sub-problem, which aims at describing and predicting the spatial-temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers. Several traffic flow models, including the Lighthill-Whitham-Richards network model accommodating vehicle spillback, have been analyzed in depth along with their solution representation established and qualitative properties shown. The corresponding DNL models are expressed as systems of differential algebraic equations. Existence, uniqueness, and well-posedness of the DNL solutions are discussed in a qualitative way.;As applications of the established modeling framework, we present and solve several network design problems including congestion pricing and dynamic signal control, where traffic-derived emissions are modeled and constrained in a mathematically tractable way to assess environmental sustainability. The numerical results reveal various types of complexity inherent in the transportation networks, and provide insights into the management of such systems.