Partially observable Markov decision process for perimeter control based on a stochastic macroscopic fundamental diagram

The use of a macroscopic fundamental diagram (MFD) for perimeter control is an effective strategy for managing traffic flow on regional road networks. However, existing methods either assume a MFD with low scattering or assume complete availability of information, which is not realistic. In order to address these limitations, we propose a novel approach that incorporates a stochastic evolution dynamic into the MFD and introduces a partially observable Markov decision process for perimeter control. Our approach assumes that the MFD is randomly distributed between upper and lower boundaries, characterized by a physically interpretable parameter, and that real-time observations represent cumulative data in specific regions. We focus on three subobjectives: minimizing travel time, minimizing capacity loss due to hysteresis, and preventing gridlock. By utilizing the Bellman equation, we solve the problem and demonstrate that our proposed control method enhances trip completion rates by 7.2% compared to the benchmark case without perimeter control. Furthermore, the inclusion of stochasticity leads to an additional 1.2% improvement in trip completion rates. Through extensive numerical tests, we establish the effectiveness of our approach in optimizing traffic flow regulation on regional road networks.