A linear framework for dynamic user equilibrium traffic assignment in a single origin-destination capacitated network

•Develop a novel mathematical framework for studying DTA problems in a dynamic capacitated network that applies to both the SO and UE formulations in a unified manner.•Prove that in the limit, the SO objective could be used to obtain the UE solution as the time step goes to zero, given the satisfaction of the FIFO constraint.•Show that the difference between the UE and SO objectives can be used as a measure to evaluate the accuracy of the approximation.•Propose an incremental solution method to effectively solve the non-linear path-based UE-DTA problem as a sequence of linear link-based SO-DTA problems where the convergence is guaranteed with a predetermined number of iterations.