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Moving in the dark: Mathematics of complex pedestrian flows
Karlstad University, Faculty of Health, Science and Technology (starting 2013).
2023 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The field of mathematical modelling for pedestrian dynamics has attracted significant scientific attention, with various models proposed from perspectives such as kinetic theory, statistical mechanics, game theory and partial differential equations. Often such investigations are seen as being a part of a new branch of study in the domain of applied physics, called sociophysics.

Our study proposes three models that are tailored to specific scenarios of crowd dynamics. Our research focuses on two primary issues. The first issue is centred around pedestrians navigating through a partially dark corridor that impedes visibility, requiring the calculation of the time taken for evacuation using a Markov chain model. The second issue is posed to analyse how pedestrians move through a T-shaped junction. Such a scenario is motivated by the 2022 crowd-crush disaster took place in the Itaewon district of Seoul, Korea. We propose a lattice-gas-type model that simulates pedestrians’ movement through the grid by obeying a set of rules as well as a parabolic equation with special boundary conditions.

By the means of numerical simulations, we investigate a couple of evacuation scenarios by evaluating the mean velocity of pedestrians through the dark corridor, varying both the length of the obscure region and the amount of uncertainty induced by the darkness. Additionally, we propose an agent-based-modelling and cellular automata inspired model that simulates the movement of pedestrians through a T-shaped grid, varying the initial number of pedestrians. We measure the final density and time taken to reach a steady pedestrian traffic state. Finally, we propose a parabolic equation with special boundary conditions that mimic the dynamic of the pedestrian populations in a T-junction. We solve the parabolic equation using a random walk numerical scheme and compare it with a finite difference approximation. Furthermore, we prove rigorously the convergence of the random walk scheme to a corresponding finite difference scheme approximation of the solution.

Place, publisher, year, edition, pages
2023.
Keywords [en]
Mathematical modelling of pedestrian dynamics, stochastic systems, evacuation time, random walk method, parabolic equation, finite difference method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-95347OAI: oai:DiVA.org:kau-95347DiVA, id: diva2:1768730
External cooperation
University of L'Aquila, Italy
Presentation
2023-06-02, 19:59 (English)
Supervisors
Examiners
Available from: 2023-06-22 Created: 2023-06-15 Last updated: 2023-06-27Bibliographically approved

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Master_thesis_MSV(4512 kB)75 downloads
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Type fulltextMimetype application/pdf

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Faculty of Health, Science and Technology (starting 2013)
Computational Mathematics

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
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  • Other locale
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Output format
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