Boundedly rational user equilibrium: models and applications

Abstract

Efficient transportation management requires good understanding of people's travel behavior. Most transportation planning models assume travelers are perfectly rational in decision-making. However, much of the empirical evidence from psychology, economics, and transportation has shown that perfect rationality is not realistic in modeling travelers' decision-making process. Thus existing transportation planning models may provide inaccurate predictions to transportation planners. Motivated by travelers' route choice changes in response to the reopening of the I-35W Bridge in Minneapolis, this dissertation shows that travelers are boundedly rational (BR) in making route choices. Though the BR travel behavioral model was proposed in the 1980's, empirical validation of such behavioral principle using real-world data along with a theoretical framework was non-existent. This study is dedicated to bridging these gaps from both empirical and theoretical perspectives.The first contribution of this dissertation is the empirical verification and estimation of boundedly rational route choice behavior. By analyzing recorded GPS trajectories from 143 commuters before and after the reopening of the I-35W Bridge in Minneapolis, we employ a probit model to estimate the bounded rationality parameters in Twin Cities. Despite the behavioral appeal of bounded rationality, a rigorous study of boundedly rational user equilibria (BRUE) solution has been lacking, partly due to its mathematical complexity. This research offers a systematic approach of deriving the BRUE solutions analytically on networks with fixed travel demands. Based on the definition of ε-BRUE, where ε is the indifference band for perceived travel times, we formulate the ε-BRUE problem as a nonlinear complementarity problem (NCP). With the increase of the indifference band, the path set that contains equilibrium flows will be augmented and the critical values of the indifference band to augment the path set can be identified by solving a sequence of mathematical programs with equilibrium constraints (MPEC). A novel solution method is provided to obtain the BRUE solution set and numerical examples are given to illustrate this finding. To provide guidelines to policy-makers for congestion mitigation, this research also explores an important phenomenon which should be avoided in transportation network design, i.e., Braess paradox. The classical Braess paradox was built upon the perfectly rational behavioral assumption. Under the framework of bounded rationality, each equilibrium flow pattern leads to a different total system travel time, resulting in non-unique network performance measures. Because of the non-uniqueness of BRUE solutions, which particular equilibrium pattern should be used to compare network performances before and after new roads are built remains a question. This dissertation aims to study the analytical properties of Braess paradox under bounded rationality by exploring the relationships between the occurrence of Braess paradox and the indifference band as well as the demand level. The unveiled relationships offer a guideline for transportation planners to prevent the occurrence of Braess paradox and pave the way for strategic transportation management under the bounded rationality assumption.