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

Emilio N. M. Cirillo; Matteo Colangeli; Adrian Muntean; T. K. Thoa Thieu; Emilio N. M. Cirillo; Matteo Colangeli; Adrian Muntean; T. K. Thoa Thieu

doi:10.3934/mbe.2020025

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 460-477. doi: 10.3934/mbe.2020025

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

1.
Department of Basic and Applied Sciences for Engineering, Sapienza University, Roma
2.
Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Italy
3.
Department of Mathematics and Computer Science, Karlstad University, Sweden
4.
Department of Mathematics, Gran Sasso Science Institute, L’Aquila, Italy

Received: 19 July 2019 Accepted: 10 October 2019 Published: 14 October 2019

We study the pedestrian escape from an obscure room 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 room 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 room. 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.
- pedestrian dynamics,
- evacuation,
- obscure room,
- simple exclusion dynamics,
- particle currents,
- drafting
Citation: Emilio N. M. Cirillo, Matteo Colangeli, Adrian Muntean, T. K. Thoa Thieu. A lattice model for active-passive pedestrian dynamics: a quest for drafting effects[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 460-477. doi: 10.3934/mbe.2020025

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Abstract

We study the pedestrian escape from an obscure room 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 room 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 room. 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.

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