Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery

Abstract

This study defines the price of anarchy for general reliability-based transport network design problems, which is an indicator of inefficiency that reveals how much the design objective value exceeds its theoretical minimum value due to the risk averse and selfish routing behavior of travelers. This study examines a new problem, which is a reliability-based continuous network design problem under cost recovery. In this problem, the variations of system travel time and path travel times, the risk attitudes of the system manager and travelers, congestion toll charges, capacity expansions, and cost recovery constraint are explicitly considered. The design problem is formulated as a min-max problem with the reliability-based user equilibrium constraint. It is proved that the price of anarchy for this problem is bounded above, and the upper bound is independent of travel time functions, demands, and network topology. The upper bound is related to the travel time variations, the value of reliability, and the value of time.