A Joint Information-Theoretic and Graph Learning Framework for Sensor Placement and Macroscopic Traffic State Reconstruction
Traffic sensor placement in large urban networks must balance traffic monitoring needs with limited installation, maintenance, and data-management budgets. This study develops a framework for preserving network-wide traffic information while reconstructing flow and density at unobserved links and the macroscopic fundamental diagram (MFD). The framework combines normalized mutual information (NMI) with Inductive Graph Neural Network Kriging (IGNNK). NMI quantifies lag-aware dependence between joint flow-density states, while a greedy algorithm selects sensors by balancing weighted information coverage against redundancy. An IGNNK-based bidirectional graph-diffusion model reconstructs unobserved link states and generates the MFD. The framework was evaluated against a principal component analysis (PCA) benchmark using seven hours of dynamic traffic assignment simulation data for the Chicago network, with 4,805 directed links and 420 one-minute intervals split into training, validation, and independent testing subsets. Reconstruction performance for both PCA and NMI-IGNNK varied substantially over the sensor ratios of 0.5% to 30%. PCA generally yielded lower root mean squared error (RMSE) over the 0.5%-3% range, but its errors were nonmonotonic and reached their minimum at 2%. At 3%, normalized joint RMSE was similar for PCA and NMI-IGNNK (0.100 and 0.105, respectively). NMI-IGNNK remained applicable up to 30% coverage and generally improved as coverage increased, reducing testing-subset normalized joint RMSE from 0.212 at 0.5% to 0.043 at 30%, with consistent trends over the complete analysis period. The framework integrates lag-aware, information-theoretic sensor placement based on joint flow-density states with directed graph-based reconstruction, enabling a broad range of sensor budgets in large-scale networks without strict limits on the number of sensors.