Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram

Zhang, J; Klingsch, W; Schadschneider, A; Seyfried, A · 2012 · OpenAlex-citations

DOI: 10.1088/1742-5468/2012/02/p02002

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Summary

This study investigates the ordering phenomena in bidirectional pedestrian flows and their impact on the fundamental diagram, which describes the relationship between density, speed, and flow. The research addresses a lack of consensus in existing literature regarding whether bidirectional flows differ significantly from unidirectional flows and how specific ordering structures, such as lane formation, influence these dynamics. While previous empirical studies and simulations have explored bidirectional characteristics, discrepancies remain regarding flow efficiency and the existence of jamming transitions. This work aims to clarify these issues through controlled laboratory experiments, comparing various forms of bidirectional ordering against unidirectional benchmarks. The researchers conducted experiments in a straight corridor with widths of 3.0 m and 3.6 m, involving up to 350 participants. They manipulated entrance widths and participant instructions to generate distinct flow types: Stable Separated Lanes (SSL), where opposing flows segregate autonomously; Dynamical Multi-Lanes (DML), characterized by unstable, time-varying lanes; and variations based on flow ratio balance (Balanced vs. Unbalanced). Pedestrian trajectories were extracted from video recordings using the PeTrack software. The analysis employed the Voronoi method to calculate integrated velocity and density over small spatial regions, allowing for high-resolution resolution of the fundamental diagram. This approach enabled the comparison of flow characteristics across different corridor widths, ordering types, and flow ratios, as well as a direct comparison with unidirectional flow data obtained under similar conditions. The results indicate that the specific flow concept is applicable to bidirectional streams. Within the observed density range (ρ < 2.0 m⁻²), no significant differences were found in the density-flow relationships among the various forms of bidirectional ordering, including SSL, DML, and balanced versus unbalanced flows. Corridor width also showed minimal influence on the fundamental diagram. However, a marked difference emerged when comparing bidirectional and unidirectional flows. For densities greater than 1.0 m⁻², unidirectional flows exhibited significantly higher velocities and specific flow rates than bidirectional streams. The bidirectional fundamental diagram displayed a plateau starting at ρ ≈ 1.0 m⁻², where flow became nearly independent of density. This plateau is attributed to "defects" caused by interactions between opposing pedestrians, which limit velocity and reduce overall flow efficiency. The study concludes that while the degree of ordering (stable vs. dynamic lanes) does not substantially alter the fundamental diagram at moderate densities, the presence of opposing flows fundamentally changes pedestrian dynamics compared to unidirectional movement. The maximum specific flow in unidirectional streams is significantly larger than in any examined bidirectional configuration. These findings imply that bidirectional flows cannot be accurately modeled as two independent unidirectional flows, even when self-organized lanes form. The interactions between opposing streams introduce constraints that reduce efficiency, highlighting the importance of accounting for counterflow interactions in pedestrian dynamics models and facility design.

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• traffic density