Properties of a well-defined macroscopic fundamental diagram for urban traffic

Geroliminis, Nikolas; Sun, Jie · 2010 · OpenAlex-citations

DOI: 10.1016/j.trb.2010.11.004

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Summary

This paper investigates the conditions under which a Macroscopic Fundamental Diagram (MFD)—a relationship linking aggregate traffic flow, density, and speed—exists for urban networks. While previous research demonstrated that MFDs exist in uniformly congested urban areas, this study addresses whether strict spatial homogeneity is required and why MFDs fail to appear in other network types, such as freeways. The authors aim to define the properties of networks that support well-defined MFDs with low scatter, thereby enabling macroscopic traffic management strategies like perimeter control. The study employs real-world data from two distinct networks: an urban arterial network in downtown Yokohama, Japan, monitored by 500 fixed sensors, and a freeway network in the Twin Cities Metropolitan Area, USA, monitored by 600 loop detectors. The authors analyze the spatial distribution of vehicle occupancy across these networks. They utilize statistical tools, including Mann–Whitney U tests and Chi-square tests, to compare occupancy distributions at different times with similar average network occupancy levels. Additionally, the authors develop an analytical model to approximate the spatial distribution of vehicles, incorporating correlations between adjacent links to account for congestion propagation, contrasting this with a standard binomial distribution assumption. The results indicate that strict homogeneity is not a necessary condition for a well-defined MFD in arterial networks. In Yokohama, occupancy distributions remained statistically similar across different times with the same average occupancy, despite spatial heterogeneity. The variance of individual detector occupancy showed a consistent relationship with average network occupancy. Conversely, the freeway network in Minnesota did not exhibit a well-defined MFD. The data revealed significant hysteresis effects, where traffic states followed different paths during the onset and offset of congestion. Statistical tests confirmed that occupancy distributions for freeways with similar average occupancy but different flows were significantly different, driven by higher spatial variance. The analytical model, which accounts for spatial correlation between links, successfully approximated the empirical occupancy distributions in the arterial network, outperforming the uncorrelated binomial model. The significance of this work lies in clarifying the structural requirements for macroscopic traffic modeling. It demonstrates that while arterial networks can support invariant MFDs despite spatial heterogeneity, freeway networks cannot due to hysteresis and inconsistent congestion distribution. This distinction is crucial for traffic management, as it validates the use of MFD-based control strategies for urban arterials while highlighting their limitations for freeway systems. The proposed analytical framework provides a method to estimate spatial vehicle distributions by accounting for link correlations, offering a theoretical basis for understanding MFD scatter and shape.

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• traffic density