Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology

This paper reviews studies that deal with properties of dynamic user equilibrium (DUE) solutions to understand the extent to which they have been resolved in past studies and indicate theoretical problems that remain to be addressed in future research. DUE assignment is an equilibrium-based methodology for dynamic traffic assignment. In conventional equilibrium-based static traffic assignment, the four desirable properties of solutions - existence, uniqueness, stability of solutions, and the existence of a robust solution methodology - are all guaranteed. These properties must be ensured for planners to obtain a reliable solution for equilibrium-based assignment. Meanwhile, for DUE assignment, although some of these properties have been proved, many issues regarding these properties remain unresolved. This paper reviews studies that deal with these properties to understand how far they have been investigated and discusses what is required from future research to improve the robustness of DUE assignment.