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From Crowd Dynamics to Crowd Safety: A Video-Based Analysis
Anders Johansson, Dirk Helbing, Habib Z. Al-Abideen, Salim Al-Bosta
TL;DR
Extreme crowding lacks sufficient empirical evidence for reliable safety and capacity assessment. This paper develops and applies video-based measurements to dense pilgrimage crowds, finding finite motion at local densities of 10 persons per square meter and identifying dynamics relevant to crowd criticality.
Problem
Empirical studies of critical conditions in human crowds are scarce, while existing pedestrian measurements and flow–density assumptions inadequately cover extreme densities relevant to safety and facility design.
Method
The paper evaluates high-density pilgrimage video using automated tracking, local density and flow measurements, and manual-count validation.
Results
At local densities of 10 persons per square meter and more, average crowd motion remained finite, while congested flow breakdown was associated with stop-and-go waves and crowd turbulence.
Takeaways & Limitations
Pressure, defined as density times velocity variance, is presented as a better indicator of critical crowd conditions than density alone.
Takeaways & Limitations
The reported measurement uncertainty includes both automated-count error and temporal variation between manual counts; for T = 10 minutes, the standard deviation was 12 percent.
Abstract
from arXiv · showhide
The study of crowd dynamics is interesting because of the various self-organization phenomena resulting from the interactions of many pedestrians, which may improve or obstruct their flow. Besides formation of lanes of uniform walking direction and oscillations at bottlenecks at moderate densities, it was recently discovered that stop-and-go waves [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)] and a phenomenon called "crowd turbulence" can occur at high pedestrian densities [D. Helbing et al., Phys. Rev. E 75, 046109 (2007)]. Although the behavior of pedestrian crowds under extreme conditions is decisive for the safety of crowds during the access to or egress from mass events as well as for situations of emergency evacuation, there is still a lack of empirical studies of extreme crowding. Therefore, this paper discusses how one may study high-density conditions based on suitable video data. This is illustrated at the example of pilgrim flows entering the previous Jamarat Bridge in Mina, 5 kilometers from the Holy Mosque in Makkah, Saudi-Arabia. Our results reveal previously unexpected pattern formation phenomena and show that the average individual speed does not go to zero even at local densities of 10 persons per square meter. Since the maximum density and flow are different from measurements in other countries, this has implications for the capacity assessment and dimensioning of facilities for mass events. When conditions become congested, the flow drops significantly, which can cause stop-and-go waves and a further increase of the density until critical crowd conditions are reached. Then, "crowd turbulence" sets in, which may trigger crowd disasters.
1. Introduction
The paper examines how pedestrian crowds form collective patterns and why existing flow–density measurements are insufficient for safety-critical extreme densities. It introduces a video-based study of pilgrimage crowds to address this empirical and capacity-design gap.
- Background: Collective pedestrian behavior can shift between qualitatively different patterns when critical system thresholds are crossed.Examples include lane formation and bottleneck oscillations, while dense crowds motivate examining transitions involving human interactions.
- Research gap: Empirical data on critical conditions in human crowds remain scarce despite the safety relevance of dense pedestrian dynamics.Dense crowds are unusually accessible to empirical analysis, but extreme crowding remains insufficiently documented.
- Research gap: Most pedestrian flow measurements cover only densities up to 4–6 persons per square meter, while conventional models assume average speed reaches zero at maximum density.One reported maximum density is 5.4 persons per square meter, and the relationship is used for facility design and evacuation studies.
- Research gap: Reports reaching 6 persons per square meter or more, alongside a projected capacity of up to 11 persons per square meter, leave the correct high-density relationship unresolved.The paper explicitly asks what happens at densities beyond the range of most measurements.
- Study aim: The study evaluates pilgrimage video recordings to explain differing flow–density curves and close the data gap in the safety-relevant range of extreme densities.It also examines whether measurements from the pilgrimage setting transfer to Western European conditions.
- Study aim: The paper emphasizes that reliable video evaluation and crowd-dynamics measures are needed because criticality depends on dynamics rather than density, speed, or flow alone.The authors developed algorithms for hundreds of pedestrians and used extensive data, manual validation, and calibration.
2. Measurement Site and Video Tracking
The study analyzes exceptionally dense pilgrimage crowds using high-mounted video and purpose-built tracking algorithms. Automated head detection, trajectory estimation, local measurements, and manual validation support analysis of crowd flow and dynamics.
- Measurement site: More than 2 terabytes of video from 12 fixed high-pole cameras documented pilgrimage conditions, with emphasis on the crowded entrance to the old Jamarat Bridge.The recordings covered the 10th to 12th day of Dhu al-Hijjah, 1426H, including the location of the January 12, 2006 crowd disaster.
- Measurement site: The entrance-area camera was selected because it showed the highest densities and most interesting crowd dynamics among the available recordings.Figure 1 identifies the old bridge and the video-recorded area used in the study.
- Video tracking method: Existing tracking software was limited in dense crowds, where pedestrians could be hidden, lost, interchanged, or exceed several-dozen tracking capacity.Perspective correction and difficult camera positions were additional constraints.
- Video tracking method: The authors developed automated head detection using successive digital filters, neural-network verification, adaptive histogram equalization, and manual-count corrections.The processing pipeline transforms raw frames into reliable pedestrian detections.
- Video tracking method: Detected head locations are linked across frames to estimate velocities, while measured trajectories support local density, speed, flow, and pedestrian counting.The system used 25 pixels per meter and 8 frames per second, with averaging enabling small mean-speed estimates.
- Validation: Manual counts sampled 5-second sequences every 10 minutes, with two independent counters used for calibration and comparison.Figure 4 depicts the slow-motion counting procedure, while Figure 5 compares automated and manual flow over 72 hours.
3. Measurement of Local Densities, Speeds, and Flows
The paper estimates local pedestrian density, speed, and flow from video while addressing spatial variation, averaging-radius effects, and umbrella-induced occlusion. It validates corrections and shows that umbrella handling materially affects measured flows.
- Local measurement: Local density, speed, and flow are computed around pedestrian locations using spatially weighted measurements with averaging radius R.The weighting smooths measurements over a neighborhood, with 63% of neighboring pedestrians within the radius-R area contributing to the density estimate.
- Local measurement: Local measurements target conditions around individual pedestrians, whereas global values average over the recorded area.Local density is treated as behaviorally relevant, while sufficiently large-radius averages reproduce global density and reduce variance.
- Dealing with Umbrellas: Umbrellas hide pedestrians in video, producing density variations that require separate corrections for global and local measurements.Global density can be corrected when umbrella fraction and average umbrella area are known, but local correction is complicated by spatially varying coverage.
- Dealing with Umbrellas: Removing the lowest-density fraction γ addresses umbrella-induced underestimation, with γ = 0.95 selected for subsequent local-density analysis.Simulations show γ = 0.95 reproduces actual densities well, whereas smaller cutoffs tend to underestimate them.
- Dealing with Umbrellas: Umbrella correction substantially increases local-flow estimates, while speed-density relationships vary relatively little with the cutoff.Because density enters flow multiplicatively, fitting speed-density data alone can yield unreliable flow-density conclusions.
4. Empirical Findings
The video analysis finds pedestrian motion persisting at extreme local densities, but congestion causes a major flow reduction and makes capacity assessment sensitive to measurement scale and population context. Comparisons with other studies show that scaled speed-density relations are more compatible than flow-density relations.
- 4. Empirical Findings: Local density distributions vary substantially, and maximum densities can be roughly twice the average density.Because safety depends on maximum occurring density rather than average density, density variability is important for evaluating crowd conditions.
- 4.1. Relationships between Densities, Velocities, and Flows: Average local speed remains nonzero at local densities of 10 persons per square meter, while pedestrians may stop only briefly.Average flows therefore remain finite with short interruptions, contrasting with the assumed zero-speed limit in vehicle-traffic analogies.
- 4.1. Relationships between Densities, Velocities, and Flows: A factor-of-3 flow breakdown occurs when conditions become congested, reducing effective capacity and further compressing the crowd.The resulting progression can reach critical conditions and, in the worst case, lead to crowd accidents.
- 4.2. The Fundamental Diagram and its Comparison with Other Measurements: Capacity cannot be read directly from the maximum local-flow curve because local maximum flows exceed maximum average flows.The fundamental diagram based on average flow and average density is therefore used for capacity assessment.
- 4.2. The Fundamental Diagram and its Comparison with Other Measurements: The measured maximum global densities are higher and average speeds lower than in many previous publications.The authors attribute differences to factors including local versus global measurements, body-size distributions, and cultural backgrounds.
- 4.2. The Fundamental Diagram and its Comparison with Other Measurements: Scaled speed-density data from different locations are reasonably compatible, whereas flow-density compatibility is less clear at extreme densities.For the authors’ data, the fitted parameters are V0 = 0.60 m/s and ρmax = 10.79 persons/m2.
5. Warning Signs of Critical Crowd Conditions
Video analysis identifies a progression from stop-and-go waves to crowd turbulence as density rises, while crowd pressure provides the clearest warning of critical conditions. Conventional density and velocity-field measures do not reliably identify when and where hazards occur.
- Stop-and-go waves: Stop-and-go waves emerged suddenly from laminar flow upstream of the 44-meter-wide Jamarat Bridge entrance, propagated over more than 30 meters, and coincided with a significant flow drop.The waves persisted for more than 20 minutes and reflected the onset of congestion.
- Crowd turbulence: After flow breakdown, density increased further and motion transitioned from stop-and-go waves to irregular crowd turbulence involving unintended displacements in all directions.Some individuals stumbled as physical crowd forces moved people involuntarily.
- Operational implications: Average density and velocity-field inspection are insufficient because local densities vary considerably and divergence and curl show no indication of the accident’s time or location.This limits the reliability of visual surveillance and conventional field-based indicators for detecting critical conditions.
- Warning indicators: Crowd pressure—density multiplied by speed variance—identifies critical locations and times more effectively than density, velocity divergence, or vorticity alone.The paper distinguishes this gas-kinetic pressure from mechanical pressure experienced in a crowd.
- Warning indicators: The crowd accident began about 10 minutes after turbulent motion started, when pressure exceeded the R-dependent threshold of 0.02/s^2.The average flow had already fallen below the R-dependent threshold of 0.8 pilgrims per meter and second more than 30 minutes before the accident.
- Operational implications: Video-based warning signs could support anticipative interventions such as flow control, rerouting, pressure relief, or separating crowds into blocks.These measures are presented as ways to stop shockwave propagation and increase safety during mass events.
6. Summary and Discussion
The study validates video-based analysis of extreme pedestrian crowding and identifies persistent motion, congestion transitions, and pressure-based indicators of critical conditions. Its findings support calibrated monitoring and safety measures for dense mass-event crowds.
- Extreme densities and motion: 10 persons per square meter and more were measured locally, while average crowd motion remained finite at extreme densities.The authors note that people kept moving at all observed densities, though this could lead to over-critical compressions.
- Critical indicators: Pressure, defined as density times velocity variance, provides more specific information about critical areas and times than density alone.The pressure-based warning can identify potentially turbulent motion over short periods and at specific locations.
- Video analysis: A newly developed automated video method measured counts, local densities, speeds, flows, and pressures in dense crowds.The method was designed for hundreds of pedestrians and did not require tracking individuals over long distances.
- Critical crowd dynamics: Congested conditions can produce flow breakdown, stop-and-go waves, further compression, and turbulent crowd motion.Stop-and-go waves and crowd turbulence were observed across multiple locations and years rather than only once in one location.
- Monitoring and calibration: Critical thresholds depend on measurement parameters and crowd characteristics, so flow and pressure alarms require proper calibration.The paper gives critical values of 0.8m/s for flow and 0.02/s2 for pressure, while recommending earlier action when stop-and-go waves begin.