Relationship between Network Parameters and Occurrence of Braess’ Paradox

Braess’ paradox is a classical traffic assignment problem in which a counter-intuitive result is obtained: under user equilibrium, adding a link to an uncapacitated road network can downgrade the system’s performance. The travel times can increase. In this study, the authors examine the relationship between the network parameters and the occurrence of this paradox. The authors study the influence of the capacity of the connecting link and consider this relationship for a more general capacitated traffic assignment where the users are both selfish and altruistic (pursuing user-optimal and system-optimal objectives). The focus is on Wheatstone-bridge type networks, since Braess’ paradox only occurs when the network has such a structure. After deriving a nonlinear optimization model for the problem, the authors explore how system behavior is affected by the capacity expansion of the connecting link by conducting a set of computer experiments.