Near-future projections in continuous agent-based models for crowd dynamics: mathematical structures in use and their implications

TL;DR

This paper explores the mathematical foundations of continuous agent-based pedestrian models, comparing different approaches to local navigation and decision-making, and analyzing their implications through numerical simulations of head-on collision scenarios.

Contribution

It clarifies the hierarchical structure of crowd models, distinguishes between decision and physical processes, and compares three archetypical navigation approaches with numerical predictions.

Findings

Reactive, anticipatory, and game-theoretic models differ in trajectory extrapolation.

Model predictions vary with walking speed, reaction time, and courtesy.

Preserving continuity between tactical and operational levels enhances model realism.

Abstract

This paper addresses the theoretical foundations of pedestrian models for crowd dynamics. While the topic gains momentum, current models differ widely in their mathematical structure, even if we only consider continuous agent-based models. To clarify their underpinning, we first lay the mathematical foundations of the common hierarchical decomposition into strategic, tactical, and operational levels and underline the practical interest in preserving the continuity between the latter two levels by working with a floor field, rather than way-points. Turning to local navigation, we clarify how three archetypical approaches, namely, purely reactive models, anticipatory models based on the idea of times to collision, and game theory, differ in the way they extrapolate trajectories in the near future. We also insist on the oft-overlooked distinction between processes pertaining to decision-making and physical contact forces. The implications of these differences are illustrated with a comparison of the numerical predictions of these models in the simple scenario of head-on collision avoidance between agents, by varying the walking speed, the reaction times, and the degree of courtesy of the agents, notably.