Braess Paradox under the bi-objective user equilibrium

Abstract

Braess Paradox and its derivative paradoxes under the single objective decision-making assumption have been extensively studied. When the single objective decision-making assumption is replaced by bi-objective decision-making assumption, the occurrence conditions under which the Braess Paradox are unknown. The paper investigates Braess Paradox under the bi-objective user equilibrium. Firstly, the definitions of Braess Paradox and Weak Braess Paradox under the bi-objective user equilibrium are introduced. Secondly, the analytical properties of the bi-objective user equilibrium solutions and the occurrence conditions of the Braess Paradox are explored on the classical Braess network with linear link performance functions. It is proved that the occurrence conditions of Braess Paradox are dependent upon link performance parameters and travel demand on the Braess network. Finally, a numerical example is tested to demonstrate Braess Paradox under the bi-objective user equilibrium.