The emergence of macroscopic interactions between intersecting pedestrian streams

The interactions between individual pedestrians can lead to emergent effects, such as the formation of lanes in bidirectional flows. Here, we expose properties of an emergent effect at a macroscopic level, namely interactions between pedestrian streams that arise when pedestrians walk into and through four-way intersections from different directions. We propose non-spatial models for the number of pedestrians from different streams inside an intersection. Each model encodes a different hypothesis for how streams interact and can produce dynamics fundamentally distinct from the other models. By fitting our models to large experimental data sets and determining which model explains the data best, we determine when and how entire streams of pedestrians start to interact. We find that as arrival rates increase, streams start to interact and compete for space. Our results suggest that these interactions result in an even balance of pedestrian numbers across two orthogonally intersecting streams. Neither of the streams can dominate. In contrast, for four intersecting streams, our findings suggest that jams in some streams can coincide with higher flow rates in other streams and that the relative dominance of streams can switch stochastically. By adapting existing methodology, we thus present a coherent conceptual approach for investigating emergent effects in temporal dynamics at aggregated levels in pedestrian flows that could be applied to other scenarios. Our approach is flexible and uses easily measured quantities, making it highly suitable for observational data in different scenarios or deployment in applications.