The multi-fractal nature of pedestrian arrival times

TL;DR

This study reveals that pedestrian arrival times at a busy railway station exhibit multifractal scaling, indicating complex, scale-dependent correlations beyond traditional models, with implications for realistic process simulation.

Contribution

The paper introduces a multifractal analysis framework to characterize pedestrian arrivals, capturing heterogeneity and external influences across multiple timescales.

Findings

Pedestrian arrivals show clear multifractal scaling across various timescales.

Arrival processes cannot be fully described by inter-arrival time statistics alone.

The framework identifies distinct temporal regimes linked to external factors.

Abstract

Pedestrian arrival times exhibit complex temporal organization across multiple scales, shaped by working hours, transportation schedules, and collective behaviors - features often neglected in conventional pedestrian arrival models. Using a dataset comprising over 23 million pedestrian movements at a Dutch railway station, we show that arrival processes cannot be fully characterized by inter-arrival time statistics alone. Instead, we demonstrate that pedestrian arrivals exhibit clear multifractal scaling, revealing scale-dependent correlations across a broad range of timescales. To quantify these properties, we apply a framework based on generalized fractal dimensions, which captures the heterogeneous structure of arrivals beyond standard point-process descriptions. This approach enables the identification of distinct temporal regimes associated with external forcing and provides a quantitative basis for constructing more realistic synthetic arrival processes. Beyond pedestrian dynamics, this approach offers methodological relevance for understanding non-trivial arrival processes in other physical or biological systems.