Bottleneck Management Using Pricing Under Constraints

Studies of the traffic congestion have been limited to designing optimal time-varying tolls to eliminate queuing. Moreover, limited studies have considered time-varying rewards that eliminate queuing. This paper is the first to systematically analyze the social optimum under a user equilibrium as well as budget and maximum toll constraints for a single bottleneck. We cast the congestion pricing problem as a bilevel optimization problem and provide several analytical and numerical results. Specifically, we show that the bilevel optimization problem can be converted into a convex optimization problem under some weak assumptions of the schedule delay cost under an inelastic demand setting. The methodological contributions are supplemented with illustrative simulation results.