A perimeter control model of urban road network based on cooperative-noncooperative two-stage game

Perimeter control based on the macroscopic fundamental diagram (MFD) can regulate the overall demand for entering the urban road network and thus enable satisfactory operational performance. However, most previous methods primarily focus on the macroscopic perspective of the network, lack an accurate description of boundary intersections, and cannot fully consider the difference in traffic running status at different boundary intersections. To overcome this limitation, this paper proposes a two-stage game perimeter control (TSGPC) model that integrates macro and micro control based on game theory. In the first stage, to reasonably allocate regional regulation quantity to each intersection, a cooperative game model for the macroscopic network region is established, promoting overall coordination at boundary intersections. In the second stage, on the premise of ensuring the completion of the intersection regulation quantity, a non-cooperative game model for the microscopic boundary intersections is established to optimize signal timing schemes, relieving queuing congestion. In the whole process of TSGPC, the queue length predicted by the Kalman filter is used as the basis of games. Simulation results demonstrate that the TSGPC model significantly improves average queue length and time while maintaining optimal network performance. Specifically, compared with the baseline model, the average queue length and average queue time at boundary intersections are reduced by 10.10% and 29.70%, respectively.