Multiple equilibria in a dynamic traffic network

This study provides an example in which the dynamic user equilibrium (DUE) assignment of a congested road network with bottlenecks is non‐unique. In previous studies, the uniqueness of DUE assignments with the bottleneck model has been shown in limited cases such as single‐origin and single‐destination networks. Consequently, it is still an important issue whether or not uniqueness is a general property of DUE assignments. The present study describes a network in which multiple patterns of link travel time are found, thus providing a negative answer to this question. The network has a loopy structure with multiple bottlenecks and multiple origin–destination (OD) pairs. Given a certain demand pattern of departure times for vehicles leaving their origins, a non‐convex set of equilibria with a non‐unique pattern of link travel times is shown to exist.