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.

Effective traffic control methods have great potential in alleviating network congestion. Existing literature generally focuses on a single control approach, while few studies have explored the effectiveness of integrated and coordinated control approaches. This study considers two representative control approaches: ramp metering for freeways and perimeter control for homogeneous urban roads, and we aim to develop a deep reinforcement learning (DRL)-based coordinated control framework for large-scale networks. The main challenges are 1) there is a lack of efficient dynamic models for both freeways and urban roads; 2) the standard DRL method becomes ineffective due to the complex and non-stationary network dynamics. In view of this, we propose a novel meso-macro dynamic network model and first time develop a demonstration-guided DRL method to achieve large-scale coordinated ramp metering and perimeter control. The dynamic network model hybridizes the link and generalized bathtub models to depict the traffic dynamics of freeways and urban roads, respectively. For the DRL method, we incorporate demonstration to guide the DRL method for better convergence by introducing the concept of "teacher" and "student" models. The teacher models are traditional controllers (e.g., ALINEA, Gating), which provide control demonstrations. The student models are DRL methods, which learn from the teacher and aim to surpass the teacher's performance. To validate the proposed framework, we conduct two case studies in a small-scale network and a real-world large-scale traffic network in Hong Kong. The research outcome reveals the great potential of combining traditional controllers with DRL for coordinated control in large-scale networks.

Existing data-driven and feedback traffic control strategies do not consider the heterogeneity of real-time data measurements. Besides, traditional reinforcement learning (RL) methods for traffic control usually converge slowly for lacking data efficiency. Moreover, conventional optimal perimeter control schemes require exact knowledge of the system dynamics and thus would be fragile to endogenous uncertainties. To handle these challenges, this work proposes an integral reinforcement learning (IRL) based approach to learning the macroscopic traffic dynamics for adaptive optimal perimeter control. This work makes the following primary contributions to the transportation literature: (a) A continuous-time control is developed with discrete gain updates to adapt to the discrete-time sensor data. (b) To reduce the sampling complexity and use the available data more efficiently, the experience replay (ER) technique is introduced to the IRL algorithm. (c) The proposed method relaxes the requirement on model calibration in a "model-free" manner that enables robustness against modeling uncertainty and enhances the real-time performance via a data-driven RL algorithm. (d) The convergence of the IRL-based algorithms and the stability of the controlled traffic dynamics are proven via the Lyapunov theory. The optimal control law is parameterized and then approximated by neural networks (NN), which moderates the computational complexity. Both state and input constraints are considered while no model linearization is required. Numerical examples and simulation experiments are presented to verify the effectiveness and efficiency of the proposed method.