In this paper, we study the preferences for uncertain travel time in which the probability distribution may not be fully characterized. In evaluating an uncertain travel time, we explicitly distinguish between risk, where probability distribution is precisely known, and ambiguity, where it is not. In particular, we propose a new criterion called ambiguity-aware CARA travel time (ACT) for evaluating uncertain travel time under various attitudes of risk and ambiguity, which is a preference based on blending Hurwicz criterion and Constant Absolute Risk Aversion (CARA). More importantly, we show that when the uncertain travel times of the links along the paths are independently distributed, finding the path that minimizes travel time under the ACT criterion is essentially a shortest path problem. We also study the implications on Network Equilibrium (NE) model where the travelers on the traffic network are characterized by their knowledge of the network uncertainty as well as their risk and ambiguity attitudes under ACT. We derive and analyze the existence and uniqueness of the solution under NE. Finally, we also obtain the Price of Anarchy that characterizes the inefficiency of this new equilibrium.
Working paper, December/2010