Scaling methods for estimating macroscopic fundamental diagrams in urban networks with sparse stationary sensor coverage

Accurately estimating traffic variables across unequipped portions of a network remains a significant challenge due to the limited amount of sensors-equipped links, such as loop detectors and probe vehicles. A common approach is to apply uniform scaling, treating unequipped links as equivalent to equipped ones, which leads to a strong bias in MFD estimation. Two alternative approaches are proposed: (1) Hierarchical network scaling and (2) Variogram-based data imputation. The hierarchical scaling method categorizes the network into several clusters according to spatial and functional characteristics, applying tailored scaling factors to each category. The variogram-based imputation leverages spatial correlations to estimate traffic variables for unequipped links, capturing spatial dependencies in urban road networks. Validation results show that the hierarchical scaling approach yields the most accurate estimates, demonstrating reliable performance with as little as 5% uniform detector coverage, while the variogram model fails to provide estimates. While the variogram-based method provides strong results with over 10% detector coverage, it is slightly less effective than the hierarchical scaling approach but performs better than the baseline non-hierarchical method.