Conflict Avoidance in Pedestrian Merging in Controlled Experiments by Variance Indicator

Abstract

Pedestrian congestion at corridor intersections often originates from localized fluctuations in motion rather than from a macroscopic collapse of flow. Understanding pedestrian instability at corridor intersections remains challenging because existing studies mainly rely on density, average speed, or flow-based measures and limited datasets, making it difficult to separate geometric turning effects from interaction induced fluctuations in merging flows. In particular, the mechanism underlying the turning angle dependence in T junctions has not been resolved. Here, we analyze more than 300 controlled experiments conducted in L corridors with turning only and T corridors with turning and merging. Using Voronoi-based speed variance $V_s$ and velocity variance $V_v$, we systematically compare geometric and interaction effects. $V_s$ effectively captures interaction driven instability, while $V_v$ reflects directional adjustments due to geometry. The comparison reveals distinct fluctuation mechanisms and identifies a critical transition near $90°$, demonstrating the advantage of variance-based indicators for diagnosing pedestrian dynamics.

Figures (13)

• Figure 1: Illustration of the Voronoi-based definition of local regions and neighbors for pedestrian $i$. Blue dots represent pedestrian centroid positions (generator points) extracted from the trajectory data. The plane is partitioned into Voronoi cells (black polygons), where each cell contains all points closer to its associated pedestrian than to any other. The highlighted red cell denotes the Voronoi region $V_i$ of the target pedestrian $i$. Surrounding red-outlined polygons indicate the Voronoi neighbors $\{\, j \in \mathcal{N}_i \,\}$, defined as pedestrians whose cells share a common boundary with $V_i$. These neighbors ($j=1, 2,3,4,5,6,7$ in the figure) form the local interaction set used in the computation of speed variance $V_s$ and velocity variance $V_v$. The shared edges represent the perpendicular bisectors of pedestrian pairs, forming the physical competition boundaries for available space.
• Figure 2: Empty corridor layouts used for constructing the turning and merging experimental geometries.(a) Corridor configuration used to create the 30° and 150° turning scenarios. Pedestrians entering from the lower branch experience a 30° left turn, while reversing the direction yields a 150° right turn. (b) Corridor configuration for generating 60° and 120° turning angles. A 60° left turn is formed for pedestrians approaching from the lower branch, and the same geometry produces a 120° right turn when traversed in the opposite direction. (c)The corridor configuration corresponding to the 90° turning case.
• Figure 3: Experimental layout of the L corridor (turning-only scenario). The corridor consists of two straight segments of equal width (2 m) connected by a turning angle, forming an L-shaped geometry. An 8 m start area and a 4 m acceleration zone are placed upstream to allow pedestrians to reach a stable walking speed before entering the measurement region. After negotiating the turn, pedestrians walk through an additional 4 m downstream segment to avoid premature deceleration.
• Figure 4: Experiment setup of merging T corridor. Two pedestrian streams enter the corridor from separate branches and merge at the junction. Pedestrians in Corridor A walk straight into the merging point, while pedestrians in Corridor B approach the intersection and turn by a prescribed angle before joining the main stream. Each branch includes a 4 m acceleration zone to ensure stable entry speeds. After the merging point, both groups share the same downstream corridor. Finally, pedestrians walk through an additional 4 m downstream segment to avoid premature deceleration.
• Figure 5: Spatial distributions of time-averaged Voronoi density in the (a) L corridor for 24-pedestrian experiments. and (b) T corridor for five turning angles for 40-pedestrian experiments. From left to right, panels correspond to turning angles of 30°, 60°, 90°, 120°, and 150°. Colorbars indicate the magnitude of the Voronoi density, with values ranging from low (blue) to high (red). In each panel, red arrows denote the walking directions of the pedestrian stream(s), and the symbol $\theta$ marks the prescribed turning angle of the corridor geometry. All maps are displayed on a fixed spatial grid covering the measurement region.