Modelling of self-driven particles: foraging ants and pedestrians

TL;DR

This paper presents unified stochastic models for ant trail formation and pedestrian movement, revealing non-monotonic speed-density relations and connecting ant behavior to evacuation dynamics through floor field models.

Contribution

It introduces a unified modeling framework for ants and pedestrians using local rules, analyzes non-monotonic speed behavior, and links ant trail models to pedestrian evacuation models.

Findings

Ant trail model exhibits non-monotonic speed-density dependence.

Experimental validation with robots confirms the model's predictions.

Floor field model generalizes ant trail behavior to pedestrian evacuation.

Abstract

Models for the behavior of ants and pedestrians are studied in an unified way in this paper. Each ant follows pheromone put by preceding ants, hence creating a trail on the ground, while pedestrians also try to follow others in a crowd for efficient and safe walking. These following behaviors are incorporated in our stochastic models by using only local update rules for computational efficiency. It is demonstrated that the ant trail model shows an unusual non-monotonic dependence of the average speed of the ants on their density, which can be well analyzed by the zero-range process. We also show that this anomalous behavior is clearly observed in an experiment of multiple robots. Next, the relation between the ant trail model and the floor field model for studying evacuation dynamics of pedestrians is discussed. The latter is regarded as a two-dimensional generalization of the ant trail model, where the pheromone is replaced by footprints.