Generalized Multi-hop Traffic Pressure for Heterogeneous Traffic Perimeter Control

Perimeter control (PC) prevents loss of traffic network capacity due to congestion in urban areas. Homogeneous PC allows all access points to a protected region to have identical permitted inflow. However, homogeneous PC performs poorly when the congestion in the protected region is heterogeneous (e.g., imbalanced demand) since the homogeneous PC does not consider specific traffic conditions around each perimeter intersection. When the protected region has spatially heterogeneous congestion, one needs to modulate the perimeter inflow rate to be higher near low-density regions and vice versa for high-density regions. A na\"ive approach is to leverage 1-hop traffic pressure to measure traffic condition around perimeter intersections, but such metric is too spatially myopic for PC. To address this issue, we formulate multi-hop downstream pressure grounded on Markov chain theory, which ``looks deeper'' into the protected region beyond perimeter intersections. In addition, we formulate a two-stage hierarchical control scheme that can leverage this novel multi-hop pressure to redistribute the total permitted inflow provided by a pre-trained deep reinforcement learning homogeneous control policy. Experimental results show that our heterogeneous PC approaches leveraging multi-hop pressure significantly outperform homogeneous PC in scenarios where the origin-destination flows are highly imbalanced with high spatial heterogeneity. Moveover, our approach is shown to be robust against turning ratio uncertainties by a sensitivity analysis.