Generalized Multi-hop Traffic Pressure for Heterogeneous Traffic Perimeter Control

TL;DR

Experimental results show that 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.

Abstract

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 naïve 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.

Figures (13)

• Figure 1: Generic and specific schemes showing 1-hop pressure is myopic for perimeter control and the need for multi-hop pressure.
• Figure 2: Two-stage control scheme: The first stage is a homogeneous controller (a pre-trained deep reinforcement learning model) that generates total permitted inflow. The second stage is a heterogeneous controller that redistributes the total permitted inflow as per multi-hop pressure at each feeder link.
• Figure 3: The pre-trained control policy for the first stage macroscopic (homogeneous) controller.
• Figure 4: Toy network used for multi-hop pressure explanation. In Figure (a), there is no network beyond what is illustrated. In Figure (b), each vertex represents a traffic link, and each edge represents the connection of links, and the weights shown on the edges are the fabricated turning ratios. The vertex $\Omega$ is the supersink, and the edges in dashed lines represent graph $G^e$ is extended from graph $G$.
• Figure 5: Tested traffic network. The protected region is bounded by a red rectangle as a perimeter. To generate imbalanced demand, the protected region is marked by two equal-sized upper and lower subregions, rendered in yellow and purple, respectively.

Theorems & Definitions (2)

• Definition 1: Graph representation
• proof