Road tolling problem on a two-link parallel network based on the fundamental diagram

This paper studies a road tolling problem in which a road user travels from A to B either via road 1 by paying or via road 2 without charge. The route choice also obeys the user-equilibrium principle. However, the travel time is formulated as a strictly increasing function of the density through the velocity-density relationship or fundamental diagram, which significantly improves the formulation in the classical traffic assignment problem. Accordingly, the influence of toll rate on the road users, the administration department and the road runner is analyzed in detail, by assuming that the user demand is rigid and maximizing the total traffic flow and the runner's benefits from the collection of toll fees.