Source-linked AI summary
New insights into pedestrian flow through bottlenecks
Armin Seyfried, Tobias Rupprecht, Oliver Passon, Bernhard Steffen, Wolfram Klingsch, Maik Boltes
TL;DR
Pedestrian bottleneck capacity estimates differ, and prior evidence challenges continuous specific-flow assumptions and the usual jam criterion. The paper experimentally studies controlled unidirectional flow across bottleneck widths, finding linear flow growth with width and jams even below the fundamental-diagram maximum.
Problem
Capacity-estimation procedures differ considerably, while reported stepwise capacity growth and the conventional jam criterion challenge established bottleneck assumptions.
Method
The study experimentally measures unidirectional pedestrian flow through laboratory bottlenecks of different widths using velocities, densities, time gaps, and controlled runs.
Results
Flow and bottleneck capacity grow approximately linearly with width, while jamming can occur even when incoming flow remains below the fundamental-diagram capacity.
Takeaways & Limitations
The results indicate that the basic bottleneck-capacity assumption used in planning guidelines must be revised.
Takeaways & Limitations
The authors state that an improved data basis is needed for a final judgment, and that preference for larger pedestrian distances remains future research.
Abstract
from arXiv · showhide
Capacity estimation is an important tool for the design and dimensioning of pedestrian facilities. The literature contains different procedures and specifications which show considerable differences with respect to the estimated flow values. Moreover do new experimental data indicate a stepwise growing of the capacity with the width and thus challenge the validity of the specific flow concept. To resolve these differences we have studied experimentally the unidirectional pedestrian flow through bottlenecks under laboratory conditions. The time development of quantities like individual velocities, density and individual time gaps in bottlenecks of different width is presented. The data show a linear growth of the flow with the width. The comparison of the results with experimental data of other authors indicates that the basic assumption of the capacity estimation for bottlenecks has to be revised. In contradiction with most planning guidelines our main result is, that a jam occurs even if the incoming flow does not overstep the capacity defined by the maximum of the flow according to the fundamental diagram.
1 Introduction
The introduction frames pedestrian bottleneck capacity estimation as practically important but methodologically inconsistent. It examines whether capacity grows continuously or stepwise with width and questions whether jams require incoming flow to exceed capacity.
- Capacity estimation supports the dimensioning and evaluation of pedestrian facilities, including minimum emptying time and facility width.
- Capacity is defined as the maximum flow, while common practice assumes jams occur only when incoming flow exceeds bottleneck capacity.The continuity equation establishes this capacity as an upper limit for incoming flow producing a jam, but does not exclude jams at smaller flows.
- The specific flow Js is calculated as average density ρ multiplied by average pedestrian speed v, implying capacity scales linearly with bottleneck width.This follows from the assumed universal fundamental diagram for Js across widths.
- Prior data suggest lane spacing is width-independent, which would make capacity increase stepwise as additional lanes form rather than continuously.The study tests this claim, particularly for bottlenecks of different widths.
- Existing capacity estimates differ substantially across guidelines, specifications, and experimental measurements.The comparison includes SFPE, Predtechenskii and Milinskii, Weidmann, Hoogendoorn, and measurements by Kretz, Nagai, and Müller.
2 Experimental setup
The experiment isolates bottleneck width as the principal variable in controlled unidirectional pedestrian-flow runs. It varies width from 0.8 m to 1.2 m and tests groups of 20, 40, and 60 pedestrians.
- The setup prioritized equal conditions across runs while measuring the influence of bottleneck width and the effect of test-group size.The study used an auditorium arrangement with desks defining the corridor and bottleneck.
- The bottleneck was 2.8 m long, with constant hip-to-shoulder width and holding areas that standardized the initial pedestrian density.The first holding area was centered three meters from the bottleneck entrance.
- Video cameras recorded the experimental configuration, including holding and measurement areas and the 0.8 m bottleneck condition.
- Widths ranged from 0.8 m to 1.2 m in 0.1 m increments, with three runs at each width using 20, 40, or 60 pedestrians.The design comprised 18 runs in total.
3 Data analysis
The analysis combines bottleneck crossing times with manually reconstructed pedestrian trajectories to examine specific flow, lane formation, time gaps, and transient velocity–density changes. Across widths, the observations support continuous rather than stepwise flow variation, while wider bottlenecks can fail to reach stationarity within the experiment.
- 3.1 Specific flow: Specific flow Js is calculated by dividing the measured pedestrian flow by bottleneck width b.The crossing interval runs from the first to the last pedestrian at the bottleneck center, y = 0.4 m.
- 3.2 Trajectories and probability distributions: Manual head-center tracking from overhead video produces individual trajectories for subsequent flow and time-gap analysis.The coordinate system is rotated and translated to the bottleneck reference frame.
- 3.3 Time dependence of ρ, vi, and ∆ti: The analysis uses individual trajectory points, time gaps between following pedestrians, and a measurement-section density to characterize microscopic flow dynamics.Density is based on the momentary number of pedestrians in the observation section, while time gaps are evaluated at the bottleneck center.
- 3.2 Trajectories and probability distributions: For N = 60, lane separation grows continuously with width, while time-gap distributions broaden and drift toward smaller gaps; no stepwise flow change is indicated.Lanes become observable for b ≥0.9 m, with the transition from one to two lanes as the only discontinuous visual change.
- 3.3 Time dependence of ρ, vi, and ∆ti: For N = 60 and b = 1.1 m, velocity decreases and density increases over time, whereas time-gap trends are difficult to identify because the changes largely compensate.Small observation-area counts create large density fluctuations, and zipper-effect jumps obscure possible time dependence in the gaps.
- 3.3 Time dependence of ρ, vi, and ∆ti: For b ≥1.0 m, even N = 60 does not reach a stationary state, so more participants or additional data are needed for a final judgment.The regression describes the overall temporal decrease but not density fluctuations or stable-state velocity fluctuations; no error margins are quoted.
4 Combined analysis with data from other experiments
Comparing laboratory bottleneck experiments shows that differing initial conditions help explain discrepant flow measurements, while flow increases continuously with bottleneck width. The combined analysis also questions the usual criterion that jamming begins only when incoming flow exceeds capacity.
- 4.1 Comparison with the data of other experiments: Higher initial densities produced substantially higher flows, explaining shifts between experimental datasets.For b = 1.2 m, Nagai et al. reported J increasing from 1.04 s−1 to 3.31 s−1 as ρini rose from 0.4 m−2 to 5 m−2.
- 4.1 Comparison with the data of other experiments: Bottleneck length had minor importance when comparing the authors’ centered bottleneck with Kretz’s much shorter one.The authors used lbck = 2.8 m, whereas Kretz used lbck = 0.4 m.
- 4.2 Linear dependence of flow and bottleneck-width: Across the combined measurements, flow increased linearly and continuously with bottleneck width rather than stepwise.A small edge near b = 0.7 m coincided with the onset of the zipper effect and was not evidence for general stepwise behavior.
- 4.3 The criteria for jam occurrence: Inside jams, density fluctuated between ρ = 4 to 6 m−2 independently of bottleneck width.Stationary bottleneck densities were near ρ ≈ 1.8 m−2, where some guideline fundamental diagrams reach maximum flow, but other data challenge that interpretation.
- 4.3 The criteria for jam occurrence: Jamming occurred before the maximum of the fundamental diagram was reached, despite the conventional capacity-based criterion.The authors attribute possible below-capacity jamming to flow fluctuations and local density maxima exceeding the capacity density.
5 Summary
Experiments show pedestrian flow through bottlenecks generally increases linearly and continuously with width, supporting the specific-flow approach above about 0.7 m. They also indicate that jams can occur below the maximum flow capacity, challenging standard capacity assumptions.
- Flow increases linearly and continuously with bottleneck width, except near b ≈0.7 m where the zipper effect begins.This pattern holds across different bottleneck types and initial conditions.
- For bottlenecks wider than 0.7 m, the basic flow equation combined with the specific-flow concept is justified.
- Jams may occur below maximum capacity, so insufficient facility dimensions can produce high densities even without panic.At high densities, small crowd interferences may not be balanced and can cause fatalities.