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Article: The entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationship

TitleThe entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationship
Authors
KeywordsDiscontinuous flow-density relationship
Entropy solution
LWR model
Traffic flow
WENOscheme
Issue Date2009
PublisherI N F O R M S. The Journal's web site is located at http://transci.pubs.informs.org
Citation
Transportation Science, 2009, v. 43 n. 4, p. 511-530 How to Cite?
AbstractIn this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piece- wise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives.,©2009 INFORMS.
Persistent Identifierhttp://hdl.handle.net/10722/71845
ISSN
2015 Impact Factor: 3.295
2015 SCImago Journal Rankings: 3.263
ISI Accession Number ID
Funding AgencyGrant Number
Council of the Hong Kong Special Administrative Region, ChinaHKU7187/05E
NSFC10671190
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui230026
AROW911NF-04-1-0291
W911NF-08-1-0520
NSFDMS-0510345
DMS-0809086
Funding Information:

The authors thank the anonymous associate editor and two anonymous referees for their helpful suggestions and critical and constructive comments on an earlier version of the paper. The work of the second author was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU7187/05E). The research of the third author was partially supported by NSFC Grant 10671190. The research of the fourth author was partially supported by NSFC Grant 10671190 while this author was visiting the Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China. Additional support was provided by AROGrants W911NF-04-1-0291 and W911NF-08-1-0520, as well as by NSF Grants DMS-0510345 and DMS-0809086.

References

 

DC FieldValueLanguage
dc.contributor.authorLu, Yen_HK
dc.contributor.authorWong, SCen_HK
dc.contributor.authorZhang, Men_HK
dc.contributor.authorShu, CWen_HK
dc.date.accessioned2010-09-06T06:35:41Z-
dc.date.available2010-09-06T06:35:41Z-
dc.date.issued2009en_HK
dc.identifier.citationTransportation Science, 2009, v. 43 n. 4, p. 511-530en_HK
dc.identifier.issn0041-1655en_HK
dc.identifier.urihttp://hdl.handle.net/10722/71845-
dc.description.abstractIn this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piece- wise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives.,©2009 INFORMS.en_HK
dc.languageengen_HK
dc.publisherI N F O R M S. The Journal's web site is located at http://transci.pubs.informs.orgen_HK
dc.relation.ispartofTransportation Scienceen_HK
dc.subjectDiscontinuous flow-density relationshipen_HK
dc.subjectEntropy solutionen_HK
dc.subjectLWR modelen_HK
dc.subjectTraffic flowen_HK
dc.subjectWENOschemeen_HK
dc.titleThe entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationshipen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0041-1655&volume=43&issue=4&spage=511&epage=530&date=2009&atitle=The+entropy+solutions+for+the+Lighthill-Whitham-Richards+traffic+flow+model+with+a+discontinuous+flow-density+relationshipen_HK
dc.identifier.emailWong, SC:hhecwsc@hku.hken_HK
dc.identifier.authorityWong, SC=rp00191en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1287/trsc.1090.0277en_HK
dc.identifier.scopuseid_2-s2.0-73349090579en_HK
dc.identifier.hkuros168272en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-73349090579&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume43en_HK
dc.identifier.issue4en_HK
dc.identifier.spage511en_HK
dc.identifier.epage530en_HK
dc.identifier.eissn1526-5447-
dc.identifier.isiWOS:000271944400008-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridLu, Y=24281590400en_HK
dc.identifier.scopusauthoridWong, SC=24323361400en_HK
dc.identifier.scopusauthoridZhang, M=7601556898en_HK
dc.identifier.scopusauthoridShu, CW=7202122336en_HK

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