# A pedestrian flow model with stochastic velocities: microscopic and macroscopic approaches

## TL;DR

This paper develops a stochastic pedestrian flow model that bridges microscopic social force dynamics with macroscopic conservation laws, using kinetic equations and numerical comparisons.

## Contribution

It introduces a novel hierarchical modeling approach combining microscopic and macroscopic descriptions with a new closure function.

## Key findings

- Models show similar behavior in numerical experiments
- The macroscopic model effectively captures microscopic dynamics
- The stochastic switching between stop-and-go states influences flow patterns

## Abstract

We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of conservation law type. Therefore we use a kinetic mean-field equation and introduce a new problem-oriented closure function. Numerical experiments are presented to compare the above models and to show their similarities.