# A lattice model for active--passive pedestrian dynamics: a quest for drafting effects

## TL;DR

This paper models pedestrian evacuation using a lattice gas with active and passive particles, showing that active particles with drift improve overall evacuation rates, akin to drafting effects in cycling.

## Contribution

It introduces a lattice model capturing active-passive pedestrian interactions and demonstrates how active particles enhance evacuation efficiency.

## Key findings

- Adding active particles increases evacuation rate.
- Active particles with drift improve particle flux.
- Drafting effect observed in a discrete lattice model.

## Abstract

We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is subject to a drift guiding the particles towards the exit. The drift mimics the awareness of some pedestrians of the geometry of the corridor and of the location of the exit. We provide numerical evidence that, in spite of the hard core interaction between particles -- namely, there can be at most one particle of any species per site, -- adding a fraction of active particles in the system enhances the evacuation rate of all particles from the corridor. A similar effect is also observed when looking at the outgoing particle flux, when the system is in contact with an external particle reservoir that induces the onset of a steady state. We interpret this phenomenon as a discrete space counterpart of the drafting effect typically observed in a continuum set--up as the aerodynamic drag experienced by pelotons of competing cyclists.