A capacity increasing paradox for a dynamic traffic assignment with departure time choice

This paper demonstrates that the capacity increasing paradox in a transportation networks as in Braess(1968) does also occur under non-stationary settings, in particular, under dynamic traffic assignment with endogenous time-varying origin-destination (OD) demands. Through the analyses, the analytical formulae for the solutions of the dynamic equilibrium assignment are explicitly derived for two kind of networks: the networks with a one-to-many OD pattern and the reversed networks with a many-to-one OD pattern, the formulae clarify the significant difference in the properties of the two dynamic flow patterns. This also leads us to the findings that one of the crucial conditions that determine whether the paradox occurs or not is the OD pattern of the underlying networks.