From sensor counts to OD flows: the N-Step model for urban pedestrian mobility

In this study, we introduce a novel model called the N-Step Flow Model, designed to synthetically estimate pedestrian flow between urban areas using data from sensor-based pedestrian counts. Inspired by the D8 flow algorithm commonly used in hydrology, the N-Step Flow Model distributes pedestrian flow across all neighboring tiles in a proportional manner, allowing a detailed analysis of collective urban mobility. The model was tested in Melbourne, Australia, where square and hexagonal tessellations were used to segment urban space. The synthetic flows generated were compared to those derived from the gravity model, showing broadly stable similarity patterns across representative weeks, with correspondence varying by step. The N-Step Flow Model provides an explicit stepwise redistribution view of spatial flow propagation, which may support exploratory planning analyses. The proposed approach offers a flexible method for analyzing pedestrian dynamics at a macro level, providing new aspects for developing urban planning strategies and supporting decision-making for infrastructure improvements.