Departure Time and Route Choices with Bottleneck Congestion: User Equilibrium under Risk and Ambiguity

Abstract

This paper examines commuters' departure time and route choices in the morning commute problem when travel time is described as a bounded distributional uncertainty set. The preferences towards risk and ambiguity are distinguished by adopting the ambiguity-aware constant absolute risk aversion travel time criteria. We first examine the dynamic user equilibrium for a single-route model with homogeneous risk/ambiguity preference. Compared with risk-neutral commuters, we find that departure time window is shifted earlier for the risk-averse commuters and shifted later for the risk-seeking commuters. We then study the single bottleneck with a risk-averse class and a risk-seeking class. It is shown that with a larger gap between the two classes' preferences, the congestion pattern will change from one peak to two peaks. It implies that preference heterogeneity may stagger the departure time choice and thereby relieve the average congestion. At last, we examine a two-routes problem with homogeneous preference towards risk and ambiguity. The commuters will choose between a faster route (highway) and a less risky route (local arterial). We prove that the flow distribution between the two routes will monotonically change with the maximum variation in travel time. That is, the highway flow will decrease with uncertainty on the highway for risk-averse commuters. In contrast, it will increase with uncertainty on the highway for risk-seeking commuters. The price of anarchy is analyzed in the numerical section by varying the risk preference and the ambiguity preference.