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Progress in Industrial Mathematics at ECMI 2018 pp 75–81Cite as

A Mean-Field Evacuation Simulation

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Part of the book series: Mathematics in Industry ((TECMI,volume 30))

Abstract

We discuss a mean-field simulation of an evacuation scenario. We model the crowd which needs to be evacuated using a probability measure μ. The controls are represented by external assistants formulated by ordinary differential equations. The task of evacuation is written as optimal control problem. Under the assumption that μ has an L 2-density, we state the corresponding first order optimality condition using a Lagrangian approach in the L 2-topology. Based on this we solve the problem with an instantaneous control algorithm. Simulation results of an evacuation scenario underline the feasibility of the approach and show the behaviour that is expected to fit the requirements posed by the cost functional.

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Author information

Authors and Affiliations

  1. TU Kaiserslautern, Kaiserslautern, Germany

    Claudia Totzeck

Authors
  1. Claudia Totzeck
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Correspondence to Claudia Totzeck .

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Editors and Affiliations

  1. Department of Applied Analysis and Computational Mathematics & ELTE-MTA Numnet Research Group, Eötvös Loránd University, Budapest, Hungary; Department of Differential Equations Mathematical Institute, Budapest University of Technology and Economics, Budapest, Hungary

    István Faragó

  2. Department of Applied Analysis and Computational Mathematics & ELTE-MTA Numnet Research Group, Eötvös Loránd University, Budapest, Hungary

    Ferenc Izsák

  3. Department of Applied Analysis and Computational Mathematics & ELTE-MTA Numnet Research Group, Eötvös Loránd University, Budapest, Hungary

    Péter L. Simon

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Totzeck, C. (2019). A Mean-Field Evacuation Simulation. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_10

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