Pareto efficiency of reliability-based traffic equilibria and risk-taking behavior of travelers

•Introduced the Pareto efficient route flow pattern in terms of mean and standard deviation of route travel time.•Examined the Pareto efficiency of the various reliability-based traffic equilibrium model in the literature.•Established the sufficient condition for the Pareto efficiency of the reliability based traffic equilibria models.•Introduced the mean-standard deviation indifference curve to analyze the travelers’ risk-taking behavior.

This paper investigates the Pareto efficiency of the various reliability-based traffic equilibria proposed in the literature and the risk-taking behavior of travelers. Reliability indexes such as the percentile travel time (PTT), travel time budget (TTB), mean excess travel time (METT) and the quadratic disutility function (QDF) are examined in terms of the mean and standard deviation (SD) of travel times. The downward sloping mean-SD indifference curve is introduced to geometrically analyze the risk-taking behavior of travelers. Both the diversifying and plunging behaviors of risk-averse travelers are investigated by examining the curvature of the mean-SD indifference curves at traffic equilibria based on the PTT, TTB, METT and QDF. Several specific probability distributions are adopted to elucidate the theoretical results obtained.