On How Traffic Signals Impact the Fundamental Diagrams of Urban Roads

Zhang, Chao; Li, Yechen; Arora, Neha; Osorio, Carolina · 2022 · OpenAlex-citations

DOI: 10.25368/2023.103

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Summary

This paper addresses the challenge of modeling traffic flow on signalized urban roads by refining the Fundamental Diagram (FD), a macroscopic tool relating speed, flow, and density. While previous work established parametric forms for urban FDs, the parameters lacked physical interpretability and required segment-specific data for estimation. This study extends prior research by explicitly modeling the FD’s power coefficients as functions of traffic signal settings, specifically the average green split. The goal is to provide a scalable, interpretable formulation that explains how signal plans govern congestion formation and propagation without relying on extensive local data collection. The methodology proposes a parsimonious parametric function relating space-mean speed to flow, where the traditional power coefficients ($\alpha$ and $\beta$) are defined as linear functions of the average green split ($g$). This approach assumes that fixed-time signals are a subset of actuated signals, allowing the model to apply broadly. The parameters of these linear relationships are fitted across all signalized segments within a city, rather than individually for each segment. The authors validate this formulation using empirical data from Salt Lake City, Utah, USA. The dataset comprises lane-level vehicular counts and aggregated space-mean speeds from actuated signal-controlled intersections, sourced from the Utah Department of Transportation’s Automated Traffic Signal Performance Metrics system. The analysis focuses on major traffic movements during weekday peak hours (7 am – 8 pm) with consistent cycle lengths. The results demonstrate that the proposed signal-parametrized FD closely approximates ground-truth data. Analysis of ten representative segments with green splits ranging from 0.3 to 0.8 shows that the model accurately captures how FDs shift as signal settings change. Specifically, higher green splits correspond to higher speeds for a given flow, reflecting increased flow capacity. The study confirms that the linear parameters defining the power coefficients have common values across different segments, validating the model's scalability. This indicates that the shape of the FD can be predicted based on signal plans alone, rather than requiring unique calibration for every road segment. The significance of this work lies in its ability to link traffic signal control directly to macroscopic traffic variables, offering insights into congestion dynamics. By reducing reliance on segment-specific data, the formulation facilitates broader application in urban traffic management and planning. The authors conclude that this approach enhances the interpretability of urban FDs and provides a practical tool for estimating the impact of signal setting changes. Future research directions include investigating the impact of signal coordination offsets and incorporating additional factors, such as left-turning flows, to further refine the understanding of urban traffic supply.

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• traffic density