# Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects

## TL;DR

This paper models pedestrian flow through bottlenecks using a stochastic zero-range process, revealing how microscopic dynamics and system geometry cause trapping states that limit flow at high densities.

## Contribution

It introduces a zero-range process model capturing the interplay between microscopic stochastic dynamics and bottleneck geometry, explaining flow saturation phenomena.

## Key findings

- Stationary particle current saturates at bottleneck rate at high densities.
- Trapping states emerge due to the interplay of system geometry and stochastic dynamics.
- Flow dynamics depend on the threshold parameter in the model.

## Abstract

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow trough a bottleneck via a Zero Range Process on a one dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modelled by a particular site of the lattice where the updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that, for any finite value of such threshold, the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds the bottleneck rate itself.