On Hughes' Model for Pedestrian Traffic

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dc.contributor.author Kaldawi, Fadi J
dc.date.accessioned 2022-04-05T12:14:03Z
dc.date.available 2022-04-05T12:14:03Z
dc.date.copyright 2020 en_US
dc.date.issued 2020-07-09
dc.identifier.uri http://hdl.handle.net/10725/13451
dc.description.abstract In this thesis, we explore the modeling and application of the pedestrian fl w model proposed by Roger L. Hughes in 2002, a system of a hyperbolic conservation law to describe crowd densities (ρ) and an Eikonal equation to describe the path potential (φ) of this crowd: ρt − div(ρf 2(ρ)∇φ) = 0 ||∇φ|| =1 f(p) Throughout this work, we explain this model in the context of a one dimensional walking facility, like a bridge or a hallway, and a two dimensional one, such as an open room with obstacles and obstructions. We revisit the motivation for the model, as well as properties and qualities of the resulting weak entropy so- lutions, some of which will aid in understanding numerical results. After this, we describe numerical methods to use in order to solve the eikonal equation for the path potential, then use this quantity to solve the conservation law for the density after a certain time step. With these methods established, we proceed to provide meaningful simulations in both the 1D and 2D cases, describing what our results mean from a mathematical perspective, then a real-life explanation, alongside a brief critique of the simulated situations with comments on how to improve the walking facility conditions from a design perspective. en_US
dc.language.iso en en_US
dc.subject Hughes, Roger L. -- 1951- -- Influence en_US
dc.subject Pedestrian traffic flow -- Methods en_US
dc.subject Pedestrian traffic flow -- Mathematical models en_US
dc.subject Conservation laws (Mathematics) en_US
dc.subject Lebanese American University -- Dissertations en_US
dc.subject Dissertations, Academic en_US
dc.title On Hughes' Model for Pedestrian Traffic en_US
dc.type Thesis en_US
dc.title.subtitle Interpreting Real-World Results en_US
dc.term.submitted Spring en_US
dc.author.degree MS in Applied and Computational Mathematics en_US
dc.author.school SAS en_US
dc.author.idnumber 201402403 en_US
dc.author.commembers Nour, Chadi
dc.author.commembers Takche, Jean
dc.author.department Computer Science And Mathematics en_US
dc.description.physdesc 1 online resource (x, 54 leaves) ; col. ill. en_US
dc.author.advisor El-Khatib, Nader
dc.keywords Pedestrian flow en_US
dc.keywords Pedestrian traffic en_US
dc.keywords Conservation law en_US
dc.keywords Eikonal equation en_US
dc.keywords Hughes model en_US
dc.keywords Fast-sweeping method en_US
dc.keywords Godunov scheme en_US
dc.keywords Characteristics en_US
dc.description.bibliographiccitations Bibliography: leaf 45-47. en_US
dc.identifier.doi https://doi.org/10.26756/th.2022.331
dc.author.email fadij.kaldawi@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php en_US
dc.publisher.institution Lebanese American University en_US
dc.author.affiliation Lebanese American University en_US

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