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.

基于宏观基本图（MFD）的交通模型的开发为城市网络提供了许多实时控制策略，包括基于警戒线的定价方案。但是，大多数现有的基于MFD的定价策略仅用于优化与流量相关的性能，而没有考虑运营商收取的收入。在这项研究中，我们调查了基于混合网络，城市网络和高速公路的基于警戒线的定价方案。在这个系统中，异类通勤者根据用户均衡原则选择他们的路线。运营城市网络有两种类型的运营目标：（1）优化城市网络的性能，即最大化流量。（2）最大化运营商的收入。为了比较这两个目标，我们首先将反馈控制应用于设计定价方案，以优化城市网络的性能。然后，我们制定了一个最优控制问题，以获得收益最大化的定价方案。通过数值示例，我们说明了这些定价方案之间的差异。