Braess paradox under the boundedly rational user equilibria

Abstract

The Braess paradox and its variants have been studied under the perfectly rational behavior assumption. However, when the perfect rationality assumption is relaxed to bounded rationality, which assumes that travelers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost, it remains unclear under what conditions the Braess paradox occurs. This paper fills this gap by exploring relationships between the occurrence of the Braess paradox and the indifference band as well as the demand level in the setting of the boundedly rational user equilibrium (BRUE). The definition of the Braess paradox is extended based on planners’ risk-taking attitudes, i.e., risk-averse, risk-prone and risk-neutral, due to the non-uniqueness of BRUE. The paradox occurrence conditions under different risk-taking attitudes are investigated using the classical Braess network and compared with those under the user equilibrium. Then we generalize the paradox conditions to simple and ordinary grid networks with regular Bureau of Public Roads (BPR) link performance functions. The impact of the link cost congestion sensitivity along with the indfference band on the occurrence of the Braess paradox is also studied.