Exact and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model with bounded acceleration for a class of fundamental diagrams

Handle URI:
http://hdl.handle.net/10754/562933
Title:
Exact and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model with bounded acceleration for a class of fundamental diagrams
Authors:
Qiu, Shanwen; Abdelaziz, Mohamed Ewis; Abdel Latif, Fadl Hicham Fadl; Claudel, Christian G. ( 0000-0003-0702-6548 )
Abstract:
In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.
KAUST Department:
Mechanical Engineering Program; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Bioscience Program; Distributed Sensing Systems Laboratory (DSS)
Publisher:
Elsevier BV
Journal:
Transportation Research Part B: Methodological
Issue Date:
Sep-2013
DOI:
10.1016/j.trb.2013.07.002
Type:
Article
ISSN:
01912615
Sponsors:
The authors are indebted to Jean-Baptiste Lesort for fruitful conversations regarding vehicular models and traffic flow coupling. The authors would also like to thank Ludovic Leclercq and Jean-Patrick Lebacque for fruitful conversations regarding the two-phase traffic flow model, well before this article was written. The development of a preliminary version of the algorithm presented in this article was supported both by INRETS (currently IFSTTAR), France, as well as UC Berkeley, USA.
Appears in Collections:
Articles; Bioscience Program; Electrical Engineering Program; Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorQiu, Shanwenen
dc.contributor.authorAbdelaziz, Mohamed Ewisen
dc.contributor.authorAbdel Latif, Fadl Hicham Fadlen
dc.contributor.authorClaudel, Christian G.en
dc.date.accessioned2015-08-03T11:16:04Zen
dc.date.available2015-08-03T11:16:04Zen
dc.date.issued2013-09en
dc.identifier.issn01912615en
dc.identifier.doi10.1016/j.trb.2013.07.002en
dc.identifier.urihttp://hdl.handle.net/10754/562933en
dc.description.abstractIn this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.en
dc.description.sponsorshipThe authors are indebted to Jean-Baptiste Lesort for fruitful conversations regarding vehicular models and traffic flow coupling. The authors would also like to thank Ludovic Leclercq and Jean-Patrick Lebacque for fruitful conversations regarding the two-phase traffic flow model, well before this article was written. The development of a preliminary version of the algorithm presented in this article was supported both by INRETS (currently IFSTTAR), France, as well as UC Berkeley, USA.en
dc.publisherElsevier BVen
dc.subjectBounded accelerationen
dc.subjectExact numerical schemeen
dc.subjectGrid-free numerical schemeen
dc.subjectLWR modelen
dc.subjectMacroscopic flow modelen
dc.subjectMoving bottlenecken
dc.titleExact and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model with bounded acceleration for a class of fundamental diagramsen
dc.typeArticleen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentBioscience Programen
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)en
dc.identifier.journalTransportation Research Part B: Methodologicalen
kaust.authorQiu, Shanwenen
kaust.authorAbdelaziz, Mohamed Ewisen
kaust.authorClaudel, Christian G.en
kaust.authorAbdel Latif, Fadl Hicham Fadlen
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