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Networks and Heterogeneous Media

2013, Volume 8, Issue 4: 985-1007. doi: 10.3934/nhm.2013.8.985
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Structured first order conservation models for pedestrian dynamics

  • 1.
    Siemens AG, Corporate Technology, 80200 Munich
  • Received: 01 August 2012 Revised: 01 April 2013

  • Primary: 35L65, 35Q91; Secondary: 90B10, 91D10.

  • 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.

    Citation: Dirk Hartmann, Isabella von Sivers. Structured first order conservation models for pedestrian dynamics[J]. Networks and Heterogeneous Media, 2013, 8(4): 985-1007. doi: 10.3934/nhm.2013.8.985

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  • 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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