Data-driven derivation of macroscopisc fundamental diagram from floating car trajectories.

Lu X; Zhang J; He Q; Zheng S; Su J · 2026 · PubMed Central

DOI: 10.1371/journal.pone.0342070

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Summary

This study addresses the challenge of accurately estimating the Macroscopic Fundamental Diagram (MFD) for urban road networks using sparse floating car data (FCD). Traditional methods relying on fixed loop detectors suffer from limited coverage and hardware failures, while existing FCD-based approaches often require inaccurate assumptions regarding vehicle penetration rates. The authors propose a novel, data-driven methodology that derives MFDs without prior knowledge of penetration rates by dynamically identifying intersection stop-line positions and calculating maximum queue lengths from GPS trajectories. The method utilizes spatiotemporal floating car data to estimate stop-line locations by identifying segments with the highest density of slow-moving vehicles. It then calculates the maximum queue length per signal cycle by combining the position of the last floating car in the queue with an estimated arrival rate during the remaining red light phase. This approach employs a weighted average arrival rate based on the proximity of downstream vehicles to the queue tail. To determine the total number of queued vehicles, the study establishes a speed-based nonlinear model that accounts for dynamic traffic conditions, rather than relying on static spacing assumptions. A dynamic scaling coefficient, derived from these maximum queue lengths, allows for the assumption-free estimation of total regional vehicles. Validation using real-world data from Chengdu, China, demonstrates significant improvements in accuracy. The study employed an HMM-CRF hybrid map-matching algorithm, which reduced average position error by 29% and intersection mismatch rates by approximately 40%. Queue length estimation achieved a root mean square error (RMSE) of 22.8 meters and a mean absolute percentage error (MAPE) of 18.5%. Crucially, the MFD estimation error for maximum network flow dropped from −17.5% to −3.5%, representing an 80% relative accuracy improvement. Unary cubic curves were identified as the optimal fitting model for MFD relationships, achieving an R² value of up to 0.9157. The significance of this work lies in its ability to provide high-precision MFD acquisition from sparse GPS data, overcoming the limitations of fixed detectors and penetration rate uncertainties. By enabling robust, real-time quantification of intersection queue lengths and network-wide traffic states, the methodology offers strong technical support for urban road network assessment. The findings suggest potential value for perimeter control applications and other MFD-based traffic management strategies, facilitating more effective macroscopic traffic modeling and monitoring in large-scale urban networks.

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