Structured first order conservation models for pedestrian dynamics

Dirk Hartmann; Isabella von Sivers

doi:10.3934/nhm.2013.8.985

Article Contents

2013, Volume 8, Issue 4: 985-1007. Doi: 10.3934/nhm.2013.8.985

This issue Previous Article Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes Next Article Singular perturbation and bifurcation of diffuse transition layers in inhomogeneous media, part I

Structured first order conservation models for pedestrian dynamics

Dirk Hartmann^1, and
Isabella von Sivers^1,

1.
Siemens AG, Corporate Technology, 80200 Munich

Received: July 31, 2012

Revised: March 31, 2013

Published: November 2013

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Abstract

In this contribution, we revisit multiple first order macroscopic modelling approaches to pedestrian flows and computationally compare the results with a microscopic approach to pedestrian dynamics. We find that widely used conservation schemes show significantly different results than microscopic models. Thus, we propose to adopt on a macroscopic level a structured continuum model. The approach basically relies on fundamental diagrams - the relationship between fluxes and local densities - as well as the explicit consideration of individual velocities, thus showing similarities to generalised kinetic models. The macroscopic model is outlined in detail and shows a significantly better agreement with microscopic pedestrian models. The increased realism, important for safety relevant real life applications, is underlined considering several scenarios.

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Mathematics Subject Classification: Primary: 35L65, 35Q91; Secondary: 90B10, 91D10.

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