The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

Abstract

Models using a superposition of scalar fields for navigation are prevalent in microscopic pedestrian stream simulations. However, classifications, differences, and similarities of models are not clear at the conceptual level of navigation mechanisms. In this paper, we describe the superposition of scalar fields as an approach to microscopic crowd modelling and corresponding motion schemes. We use this background discussion to focus on the similarities and differences of models, and find that many models make use of similar mechanisms for the navigation of virtual agents. In some cases, the differences between models can be reduced to differences between discretisation schemes. The interpretation of scalar fields varies across models, but most of the time this variation does not have a large impact on simulation outcomes. The conceptual analysis of different models of pedestrian dynamics allows for a better understanding of their capabilities and limitations and may lead to better model development and validation.

Investigating the Randomness of Passengers’ Seating Behavior in Suburban Trains

“…The closer they are to the seat, the higher is their utility. Distance to the seat is not measured through Euclidean distance but by computing geodesics [ 4 , 47 ] so that obstacles are skirted. Other agents cause a dip in utility so that agents keep a distance to each other.…”

“…Pedestrian dynamics span a wide field of research from empirical studies to mathematical modeling [ 1 ]. Microscopic, that is, individual-based models of human locomotion are used to simulate crowd motion and study emergent behavior (see [ 2 , 3 , 4 ] for overviews). The goal is often to improve safety by estimating evacuation times and crowd densities [ 5 , 6 , 7 , 8 , 9 ] while also optimizing efficiency in public transport.…”

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“…Existing methods for simulating pedestrian trajectories can be categorized into explicit rule‐driven and data‐driven models. Explicit rule‐driven models encode the walking mechanisms using differential equations (Helbing & Johansson, 2013; Helbing & Molnar, 1995; Hughes, 2002; Karamouzas & Overmars, 2011; Xi et al., 2011), fluid mechanic models (Henderson, 1974), queuing network process models (Løvås, 1994), or cellular automata (Blue & Adler, 2001; Lämmel & Flötteröd, 2015; Seitz et al., 2016; Yamamoto et al., 2006). The next move of a pedestrian is predicted according to the current environment and her interactions with other pedestrians.…”

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“…The spatial attractiveness is then interpreted as either potential (causing forces), utility, or probability (Seitz, Dietrich, Köster, & Bungartz, 2016). All of the models are simplifications -or idealisations -of the real world.…”

“…All of the models mentioned, except the one by Moussaïd et al (2011), are implicitly based on the idea of approach–avoidance motivation (Elliot, 2006). The spatial attractiveness is then interpreted as either potential (causing forces), utility, or probability (Seitz, Dietrich, Köster, & Bungartz, 2016). All of the models are simplifications—or idealizations—of the real world.…”