Perimeter control prevents loss of traffic network capacity due to congestion in urban areas. Homogeneous perimeter control allows all access points to a protected region to have the same maximal permitted inflow. However, homogeneous perimeter control performs poorly when the congestion in the protected region is heterogeneous (e.g., imbalanced demand) since the homogeneous perimeter control does not consider location-specific traffic conditions around the perimeter. When the protected region has spatially heterogeneous congestion, it can often make sense to modulate the perimeter inflow rate to be higher near low-density regions and vice versa for high-density regions. To assist with this modulation, we can leverage the concept of 1-hop traffic pressure to measure intersection-level traffic congestion. However, as we show, 1-hop pressure turns out to be too spatially myopic for perimeter control and hence we formulate multi-hop generalizations of pressure that look ``deeper'' inside the perimeter beyond the entry intersection. In addition, we formulate a simple heterogeneous perimeter control methodology that can leverage this novel multi-hop pressure to redistribute the total permitted inflow provided by the homogeneous perimeter controller. Experimental results show that our heterogeneous perimeter control policies leveraging multi-hop pressure significantly outperform homogeneous perimeter control in scenarios where the origin-destination flows are highly imbalanced with high spatial heterogeneity.

Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either model-based or model-free, depending on whether they rely on network transmission models (NTMs) and macroscopic fundamental diagrams (MFDs). Although model-based approaches are more data efficient and have performance guarantees, they are inherently prone to model bias and inaccuracy. For example, NTMs often become imprecise for a large number of protected regions, and MFDs can exhibit scatter and hysteresis that are not captured in existing model-based works. Moreover, no existing studies have employed reinforcement learning for homogeneous flow rate optimization in microscopic simulation, where spatial characteristics, vehicle-level information, and metering realizations -- often overlooked in macroscopic simulations -- are taken into account. To circumvent issues of model-based approaches and macroscopic simulation, we propose a model-free deep reinforcement learning approach that optimizes the flow rate homogeneously at the perimeter at the microscopic level. Results demonstrate that our model-free reinforcement learning approach without any knowledge of NTMs or MFDs can compete and match the performance of a model-based approach, and exhibits enhanced generalizability and scalability.