A dynamic traffic equilibrium assignment paradox

This paper explores the properties of dynamic flow patterns on two symmetrical networks: an `evening-rush-hour' network (E-net) with a one-to-many origin-destination (OD) pattern and a `morning-rush-hour' network (M-net) with a many-to-one OD pattern that can be obtained by reversing the direction of links and the origin and destinations of the evening-rush-hour network. Although conventional static traffic assignment produces exactly the same flow pattern for both networks, such a simple result does not hold for dynamic assignment. We show this result theoretically by using dynamic equilibrium assignment with a point queue model. Specifically, we first derive the closed form solutions of the dynamic assignment for both networks. We then identify the essential differences between the two dynamic network flow patterns by comparing the mathematical structure of the solutions. Furthermore, a type of capacity paradox (a dynamic version of Braess's paradox) is identified in order to demonstrate the differences.