Enhanced empirical data for the fundamental diagram and the flow through bottlenecks

In recent years, several approaches for modelling pedestrian dynamics have been proposed and applied e.g. for design of egress routes. However, so far not much attention has been paid to their ‘quantitative’ validation. This unsatisfactory situation belongs amongst others on the uncertain and contradictory experimental data base. The fundamental diagram, i.e. the density-dependence of the flow or velocity, is probably the most important relation as it connects the basic parameter to describe the dynamic of crowds. But specifications in different handbooks as well as experimental measurements differ considerably. The same is true for the bottleneck flow. After a comprehensive review of the experimental data base we give an survey of a research project, including experiments with up to 250 persons performed under well controlled laboratory conditions. The trajectories of each person are measured in high precision to analyze the fundamental diagram and the flow through bottlenecks. The trajectories allow to study how the way of measurement influences the resulting relations. Surprisingly we found large deviation amongst the methods. These may be responsible for the deviation in the literature mentioned above. The results are of particular importance for the comparison of experimental data gained in different contexts and for the validation of models.

💡 Research Summary

The paper addresses a critical gap in pedestrian dynamics research: the lack of reliable, quantitative validation data for the fundamental diagram (the relationship among density, speed, and flow) and for flow through bottlenecks. After a thorough review of existing literature, the authors highlight that specifications in widely used handbooks (SFPE, Weidmann, Predtechenskii‑Milinskii) and empirical studies differ dramatically. Reported maximum specific flows range from 1.2 to 1.8 (m·s⁻¹), the density at which speed drops to zero varies between 3.8 m⁻² and 10 m⁻², and the density at which flow peaks (ρ_c) spans 1.75 m⁻² to 7 m⁻². Proposed explanations include cultural and population differences, uni‑ versus bidirectional flow effects, and, importantly, the measurement methodology (time‑averaged versus space‑averaged data).

To resolve these contradictions, the authors conducted a large‑scale experimental campaign funded by the DFG, involving up to 250 participants per run, over 99 runs across five days. The participants were homogeneous (soldiers) to minimize variability. Two experimental setups were used: (1) a straight corridor of varying width to obtain the fundamental diagram under both unidirectional and bidirectional conditions, and (2) a series of bottlenecks with systematically varied width, length, and entrance distance to study the flow‑width relationship. High‑speed video recordings combined with automated trajectory extraction yielded sub‑centimeter accuracy for each pedestrian’s position over time, providing a complete microscopic dataset (positions, velocities, accelerations, local densities, and time gaps).

A central contribution is the systematic comparison of two measurement approaches. Method A (time‑average) records the number of pedestrians crossing a fixed line during a time interval Δt, yielding flow J = N/Δt and the average speed of those N individuals. Method B (space‑average) selects a spatial window Δx at a given instant, directly measuring local density ρ = N′/(w·Δx) and the mean speed of the N′ pedestrians inside the window. Applying both methods to the same trajectory data revealed discrepancies up to 20 % in flow and speed, especially at high densities where Method B captures transient crowding more accurately. This finding explains much of the spread in published fundamental diagrams and underscores the necessity of specifying the averaging procedure when reporting pedestrian flow data.

The bottleneck experiments show that for widths larger than about 0.6 m the specific flow increases almost linearly with width, contradicting earlier claims of a stepwise increase. However, the absolute flow values depend strongly on the initial density in front of the bottleneck; high upstream densities (≈ 5 m⁻²) can produce flows that exceed the maximum flow predicted by the fundamental diagram, while the density inside the bottleneck stabilizes around 1.8 m⁻². This suggests that self‑organization (lane formation) within the bottleneck can enhance throughput beyond what would be expected from a simple density‑flow relation.

In conclusion, the paper demonstrates that (1) methodological differences are a primary source of inconsistency in pedestrian flow literature, (2) high‑precision trajectory data provide a robust basis for calibrating and validating pedestrian simulation models, and (3) design guidelines should be revised to incorporate empirically derived, method‑consistent parameters. The authors propose that future work extend this standardized experimental protocol to diverse cultural contexts and more complex geometries (stairs, slopes) to further generalize the findings.