Are the objective and solutions of dynamic user-equilibrium models always consistent?

Existing dynamic user-equilibrium traffic assignment (DUETA) models are mostly expanded from the static user-equilibrium traffic assignment model by introducing the time dimension along with a group of additional constraints. Whereas the equivalency between the solution to the traffic assignment model and the user-equilibrium condition as defined by Wardrop is well established in the static case, the same may not be true for the dynamic case. This paper examines the general form of DUETA models as proposed in previous research and shows that, if queuing behavior is represented in the model at a minimal level, the solution to conventional DUETA models with an objective function of the form adopted by most existing formulations may not necessarily converge to or approximate the Wardropian user-equilibrium condition in the dynamic sense as defined by many researchers.