Price of anarchy for reliability-based traffic assignment and network design

Abstract

This study aims at investigating the impacts of supply uncertainty on the self- routing behavior of travelers when travel demands are fixed. This study proposes a distribution-free reliability-based user equilibrium traffic assignment problem that consider supply uncertainty, in which both the risk aversion of travelers and system manager are captured. It proposes a reliability-based user equilibrium model with speed limits that considers the system wide impacts of speed limits on traffic flows and travel time variations, which has not been addressed in the literature before. The price of anarchy (PoA) for the reliability-based traffic assignment problems (without and with speed limits) are defined, and upper bounds of the PoA of reliability-based traffic assignment problems with Bureau of Public Road (BPR) type travel time functions are derived. This study also extends the application of the PoA for traffic assignment problems to distribution-free reliability-based network design problems that consider supply uncertainty, which also include the traditional network design problems as a special case. It proposes capacity expansion network design problems and capacity and toll network design problems. It defines the PoAs for (reliability-based) network design problems, which is the worst-case ratio between the optimal objective function values of a reliability-based user equilibrium design and a reliability-based system optimal design. The PoAs for reliability-based network design problems are proven to be bounded above by the upper bounds of that for reliability-based traffic assignment problems of the same instance, before any link expansion.