Cordon-based pricing schemes for mixed urban-freeway networks using macroscopic fundamental diagrams

The development of traffic models based on macroscopic fundamental diagrams (MFD) enables many real-time control strategies for urban networks, including cordon-based pricing schemes. However, most existing MFD-based pricing strategies are designed only to optimize the traffic-related performance, without considering the revenue collected by operators. In this study, we investigate cordon-based pricing schemes for mixed networks with urban networks and freeways. In this system, heterogeneous commuters choose their routes based on the user equilibrium principle. There are two types of operational objective for operating urban networks: (1) to optimize the urban network’s performance, that is, to maximize the outflux; and (2) to maximize the revenue for operators. To compare those two objectives, we first apply feedback control to design pricing schemes to optimize the urban network’s performance. Then, we formulate an optimal control problem to obtain the revenue-maximization pricing scheme. With numerical examples, we illustrate the difference between those pricing schemes.