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Enhanced empirical data for the fundamental diagram and the flow through bottlenecks
A. Seyfried, M. Boltes, J. Kähler, W. Klingsch, A. Portz, T. Rupprecht, A. Schadschneider, B. Steffen, A. Winkens
TL;DR
Pedestrian-dynamics models have limited quantitative validation because empirical fundamental-diagram and bottleneck-flow data are uncertain and contradictory. The paper reviews these data and surveys controlled experiments with precise trajectory measurements, finding that measurement methods can produce large deviations in the resulting relations. These findings bear on comparing data across contexts and validating models.
Problem
Uncertain and contradictory empirical data limit quantitative calibration and validation of pedestrian-dynamics models and the interpretation of fundamental diagrams and bottleneck flow.
Method
The paper reviews empirical results and surveys controlled laboratory experiments with up to 250 people, accurately recording pedestrian trajectories and comparing measurement methods.
Results
Different measurement methods produce large deviations in the resulting pedestrian-flow relations, including discrepancies associated with averaging over time versus space.
Takeaways & Limitations
Measurement procedures matter when comparing experimental data from different contexts and validating pedestrian-dynamics models.
Takeaways & Limitations
The controlled experiments use special laboratory conditions and are not suited directly for design recommendations such as escape routes.
Abstract
from arXiv · showhide
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.
1 Introduction
Pedestrian-dynamics models require reliable empirical data for quantitative calibration and validation, yet existing measurements are uncertain and contradictory. The paper reviews these discrepancies and presents controlled experiments with precise trajectory recording to examine pedestrian dynamics and measurement effects.
- Research gap: Existing pedestrian-dynamics models lack sufficient empirical data to test and discriminate between them quantitatively.Quantitative predictions such as evacuation or travel times require calibration with empirical data.
- Research gap: The fundamental diagram relates pedestrian flow to density and is central to facility design and crowd self-organization.It is associated with phenomena including lane formation and congestion.
- Research gap: Experimental studies, guidelines, and handbooks differ in maximal flow, corresponding density, and overcrowding density.The connection between the fundamental diagram and bottleneck flow is also not well understood.
- Research gap: Limited calibration and validation, together with unclear empirical data, restrict the use of pedestrian models for applications such as safety planning.More reliable validation and calibration data are needed for quantitative computer-simulation predictions.
- Approach: The project reviews empirical discrepancies and conducts controlled experiments with up to 250 persons, recording trajectories accurately to study measurement effects.The trajectory data provide microscopic insight into pedestrian dynamics.
2 Review of Empirical Results
The review finds substantial disagreement in fundamental-diagram specifications and measurements, while bottleneck-flow studies remain controversial. Reported bottleneck flow is compatible with an almost linear width dependence, but its magnitude varies strongly across experiments and can exceed fundamental-diagram maxima.
- 2.1 Fundamental Diagram: The fundamental diagram empirically relates density ρ to flow J or specific flow Js = J/w, with equivalent velocity forms.It is a basic input for designing and dimensioning planar pedestrian facilities.
- 2.1 Fundamental Diagram: Guideline specifications and measurements disagree considerably across planar facilities.Figure 1 compares guideline curves with measurements spanning the reported range.
- 2.1 Fundamental Diagram: Js,max ranges from 1.2 (ms)−1 to 1.8 (ms)−1, while ρ0 ranges from 3.8 m−2 to 10 m−2.The density at maximum flow, ρc, ranges from 1.75 m−2 to 7 m−2.
- 2.1 Fundamental Diagram: No consensus explains discrepancies among fundamental diagrams, with proposed factors including flow direction, population, culture, fluctuations, psychology, and traffic type.Strictly unidirectional datasets from London and Osaka were reported to agree despite cultural differences.
- 2.2 Bottleneck Flow: Bottleneck-capacity dependence on width is controversial because lane-based reasoning suggests stepwise growth, whereas other observations suggest continuous variation.The comparison of laboratory experiments was intended to determine whether capacity grows continuously or stepwise.
- 2.2 Bottleneck Flow: For w > 0.6 m, collected bottleneck-flow data are compatible with a continuous and almost linear increase with width.Muir et al.'s airplane-evacuation data show nearly constant flow above 0.6 m, possibly because another process limits flow.
- 2.2 Bottleneck Flow: Bottleneck capacities differ considerably across experiments, and some measured flows exceed the maxima of empirical fundamental diagrams.Exact bottleneck geometry has minor influence, while high initial density can increase measured flow.
3 Research Project - Overview
The research project uses controlled, large-scale pedestrian experiments with high-accuracy trajectory recording to study fundamental diagrams and bottleneck flow. It varies corridor and bottleneck conditions, while acknowledging that laboratory results are not directly suited to design recommendations.
- The project combines large-scale experiments, automated high-accuracy trajectory collection, microscopic and macroscopic analysis, and quantitative pedestrian-model development.The work is a cooperation involving the execution of experiments, trajectory data collection, analysis, and model development.
- Experiments used a homogeneous group under well controlled laboratory conditions to reduce uncontrollable influences on crowd movement.The participants were soldiers, and the controlled setting was chosen to study individual parameters more reliably.
- High-accuracy trajectories provide microscopic insight and a data base for developing and verifying pedestrian-dynamics models.The authors state that laboratory conditions are not suited for direct escape-route design recommendations.
- Runs varied corridor width, flow direction, and pedestrian count to determine the fundamental diagram across the density regime.The setup included both unidirectional and bidirectional flows and different corridor widths.
- Bottleneck experiments varied bottleneck width, corridor width, and bottleneck length to analyze bottleneck flow.These parameters were changed across experimental runs.
4 Influence of the Measurement Method
The paper distinguishes local time-averaged and spatially averaged measurements of pedestrian observables, then compares them using identical trajectory data. These methods can produce substantially different fundamental diagrams, especially in high-density, inhomogeneous flow.
- Measurement methods: Different measurement methods average observables over time at a fixed location or over space at a specific time.Method A uses a cross-section and time interval ∆t; Method B uses an observation area of width w and length ∆x.
- Measurement methods: Method A directly determines flow and velocity at a cross-section, while Method B directly determines density and velocity within an observation area.The methods use different directly measured quantities before converting between fundamental-diagram representations.
- Measurement methods: The hydrodynamic relation J = ρ v w connects the representations, but the temporal and spatial mean velocities ⟨v⟩t and ⟨v⟩x do not necessarily correspond.Consequently, density inferred from flow and temporal mean velocity may differ from density measured directly over space.
- Experimental comparison: The experiments analyzed movement along a line in 12 runs with N = 17 to N = 70, including trajectory projections for N = 45, 56, and 62.Increasing N produced more unordered dynamics and intermittent stopping at constant positions; analysis was restricted to the stationary state.
- Comparison of methods: Using the same trajectories, the two methods yield visibly different fundamental diagrams, with especially clear deviations at high densities where jam waves occur.Method B used a 4 m observation area, producing discrete density values separated by ∆ρ = (4m)^−1 and large velocity fluctuations.
5 Conclusions
The study identifies substantial discrepancies in fundamental-diagram and bottleneck-flow specifications and shows that measurement methods can produce large deviations, even in a simple pedestrian system.
- Large discrepancies remain in literature specifications of the fundamental diagram and bottleneck flow, especially at high densities.
- Experiments with up to 250 people measured each pedestrian’s trajectory with high accuracy under controlled laboratory conditions.
- Different measurement methods produced large deviations for pedestrians moving along a line under periodic boundary conditions.
- The deviations arise from averaging over different degrees of freedom in a discrete system with large inhomogeneities.
- Different measurement methods may contribute to discrepancies among experimental results reported in the literature.