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Article: Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
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TitleRevisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
 
AuthorsHuang, L2
Wong, SC1
Zhang, M2
Shu, CW4
Lam, WHK3
 
KeywordsContinuum Modeling
Eikonal Equation
Pedestrian Flow
Reactive Dynamic User Equilibrium
Weno Scheme
 
Issue Date2009
 
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/trb
 
CitationTransportation Research Part B: Methodological, 2009, v. 43 n. 1, p. 127-141 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.trb.2008.06.003
 
AbstractIn this paper, we revisit Hughes' dynamic continuum model for pedestrian flow in a two-dimensional walking facility that is represented as a continuum within which pedestrians can freely move in any direction [Hughes, R.L., 2002. A continuum theory for the flow of pedestrians. Transportation Research Part B, 36 (6), 507-535]. We first reformulate Hughes' model, and then show that the pedestrian route choice strategy in Hughes' model satisfies the reactive dynamic user equilibrium principle in which a pedestrian chooses a route to minimize the instantaneous travel cost to the destination. In this model, the pedestrian demand is time varying. The pedestrian density, flux, and walking speed are governed by the conservation equation. A generalized cost function is considered. The reformulated problem is solved by the efficient weighted essentially non-oscillatory scheme for the conservation equation and the fast sweeping method for the Eikonal equation. A numerical example is used to demonstrate the effectiveness of the proposed solution procedure. © 2008 Elsevier Ltd. All rights reserved.
 
ISSN0191-2615
2012 Impact Factor: 2.944
2012 SCImago Journal Rankings: 3.080
 
DOIhttp://dx.doi.org/10.1016/j.trb.2008.06.003
 
ISI Accession Number IDWOS:000270655700009
Funding AgencyGrant Number
Hong Kong Special Administrative Region, ChinaHKU 7176/07E
PolyU 5168/04E
Chinese Academy of Sciences2004-1-8
AROW911NF-04-1-0291
NSFDMS-0510345
Funding Information:

The research of the second author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7176/07E). The research of the third author was supported by the Chinese Academy of Sciences Grant 2004-1-8. The research of the fourth author was supported by the Chinese Academy of Sciences during his visit to the University of Science and Technology of China (Grant 2004-1-8) and to the Institute of Computational Mathematics and Scientific/Engineering Computing. Additional support was provided by ARO Grant W911NF-04-1-0291 and NSF Grant DMS-0510345. The research of the fifth author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (PolyU 5168/04E).

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorHuang, L
 
dc.contributor.authorWong, SC
 
dc.contributor.authorZhang, M
 
dc.contributor.authorShu, CW
 
dc.contributor.authorLam, WHK
 
dc.date.accessioned2012-06-26T06:05:03Z
 
dc.date.available2012-06-26T06:05:03Z
 
dc.date.issued2009
 
dc.description.abstractIn this paper, we revisit Hughes' dynamic continuum model for pedestrian flow in a two-dimensional walking facility that is represented as a continuum within which pedestrians can freely move in any direction [Hughes, R.L., 2002. A continuum theory for the flow of pedestrians. Transportation Research Part B, 36 (6), 507-535]. We first reformulate Hughes' model, and then show that the pedestrian route choice strategy in Hughes' model satisfies the reactive dynamic user equilibrium principle in which a pedestrian chooses a route to minimize the instantaneous travel cost to the destination. In this model, the pedestrian demand is time varying. The pedestrian density, flux, and walking speed are governed by the conservation equation. A generalized cost function is considered. The reformulated problem is solved by the efficient weighted essentially non-oscillatory scheme for the conservation equation and the fast sweeping method for the Eikonal equation. A numerical example is used to demonstrate the effectiveness of the proposed solution procedure. © 2008 Elsevier Ltd. All rights reserved.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationTransportation Research Part B: Methodological, 2009, v. 43 n. 1, p. 127-141 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.trb.2008.06.003
 
dc.identifier.citeulike4631067
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.trb.2008.06.003
 
dc.identifier.eissn1879-2367
 
dc.identifier.epage141
 
dc.identifier.hkuros154632
 
dc.identifier.isiWOS:000270655700009
Funding AgencyGrant Number
Hong Kong Special Administrative Region, ChinaHKU 7176/07E
PolyU 5168/04E
Chinese Academy of Sciences2004-1-8
AROW911NF-04-1-0291
NSFDMS-0510345
Funding Information:

The research of the second author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7176/07E). The research of the third author was supported by the Chinese Academy of Sciences Grant 2004-1-8. The research of the fourth author was supported by the Chinese Academy of Sciences during his visit to the University of Science and Technology of China (Grant 2004-1-8) and to the Institute of Computational Mathematics and Scientific/Engineering Computing. Additional support was provided by ARO Grant W911NF-04-1-0291 and NSF Grant DMS-0510345. The research of the fifth author was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (PolyU 5168/04E).

 
dc.identifier.issn0191-2615
2012 Impact Factor: 2.944
2012 SCImago Journal Rankings: 3.080
 
dc.identifier.issue1
 
dc.identifier.scopuseid_2-s2.0-55049132227
 
dc.identifier.spage127
 
dc.identifier.urihttp://hdl.handle.net/10722/150475
 
dc.identifier.volume43
 
dc.languageeng
 
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/trb
 
dc.publisher.placeUnited Kingdom
 
dc.relation.ispartofTransportation Research Part B: Methodological
 
dc.relation.referencesReferences in Scopus
 
dc.subjectContinuum Modeling
 
dc.subjectEikonal Equation
 
dc.subjectPedestrian Flow
 
dc.subjectReactive Dynamic User Equilibrium
 
dc.subjectWeno Scheme
 
dc.titleRevisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
 
dc.typeArticle
 
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Author Affiliations
  1. The University of Hong Kong
  2. University of Science and Technology of China
  3. Hong Kong Polytechnic University
  4. Brown University