Traffic congestion is a significant issue in all urban areas with concentration of activities for various city topologies and distribution of population and land use around the world. Developing realistic models that are able to replicate congestion spreading and growth in large traffic networks is a critical step toward ameliorating traffic conditions. However, due to the complexity and unpredictability of drivers' behavior, deriving realistic models remains challenging. Moreover, as the size of the cities grows, real-time control becomes more challenging and applying centralized real-time control in all signalized intersections seems computationally impossible. Hence, hierarchical control strategies with aggregated models have recently gained a lot of interests to improve network traffic conditions. The basic concept of such an approach is to partition the heterogeneous network into a small number of homogeneous regions and control the inter-transferring flows along the boundaries between regions. This dissertation proposes methods toward clustering and control of large-scale heterogeneous urban networks.
The focus of the first part is to study how congestion spreads and propagates over space and time by partitioning heterogeneous urban networks into homogeneous and spatially compact areas. This allows us to utilize a well-defined Macroscopic Fundamental Diagram (MFD), which exists for homogeneous regions, as a reliable tool for monitoring and controlling the congestion at a macroscopic level. MFD provides an aggregated model of urban traffic dynamics linking network circulating flow and average density. Chapter 2 proposes a static method to partition network into homogeneous and compact regions, based on a newly defined similarity metric. The method captures directional congestion and is not sensitive to the network structure and parameter calibration. Chapter 3 introduces a Mixed Integer Linear formulation for static partitioning problem. The model contains homogeneity and compactness metrics in the objective function and explicitly enforces connectivity. The method can be efficiently solved and obtain Pareto optimal solutions. Chapter 4 develops a framework to replicate the congestion propagation by dynamically update clusters over time. The framework allows to find new pockets of congestion and dynamically merge regions with similar traffic patterns.
Second part of the thesis studies multi-region aggregated level modeling and control of large-scale urban networks where well-defined MFD exists for every region. Chapters 5 and 6 introduce a reformulated version of traffic dynamic systems for which the derived controllers can be implemented with limited data of loop detectors. Chapter 5 derives the optimal multivariable proportional integral feedback regulator using an adaptive optimization scheme. The adaptive fine tuning scheme is applied to tune the parameters of the controller so as to achieve a desirable performance under uncertainty and error of modeling. The proposed methodology in chapter 5 is applicable in real life as it is computationally efficient and only requires loop detector measurements. In chapter 6, a generic traffic state estimator for multi-region urban networks of arbitrary topology, characteristics, and measurement configurations is proposed. The estimation scheme is utilized by a proposed linear Model Predictive Controller to deliver the estimate of the state vector when direct measurements are not available.