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Article: Steady-state solution to the LWR model on a single origin-destination parallel road network

TitleSteady-state solution to the LWR model on a single origin-destination parallel road network
Authors
Keywordsbottleneck effects
composite links unit
Shock discontinuities
static traffic assignment
user-equilibrium conditions
Issue Date19-Apr-2024
PublisherTaylor and Francis Group
Citation
Transportmetrica B: Transport Dynamics, 2024, v. 12, n. 1 How to Cite?
Abstract

This paper describes the systematical study of a steady-state solution to the Lighthill-Witham-Richards (LWR) model on a single origin-destination parallel road network, in which the user-equilibrium condition is satisfied and shocks on links are permitted. This study derives a novel static traffic assignment model considering the complete fundamental diagram, including the congested branch. For a composite links unit that includes a set of parallel links between two junctions, the user-equilibrium condition is discussed in detail and thus, the so-called user-equilibrium curves are defined. For a single origin-destination parallel road network, we note that shock structures must be introduced to guarantee the existence of the solution when a bottleneck exists, and thus we establish the correlation between the total number of vehicles and the steady-state solution. Moreover, the uniqueness of the solution is proved by introducing priority coefficients when shocks appear. We analytically give the complete solving procedure of the steady-state solution and thus, avoid the iterative algorithms used in other static traffic assignment models. A numerical scheme of the LWR network model is designed to converge the traffic flow into the discussed steady-state solution, by determining the percentages and priority coefficients at junctions. A numerical example is given to validate the convergence for the designed numerical scheme on a road network with two 2×22×2 junctions.


Persistent Identifierhttp://hdl.handle.net/10722/342965
ISSN
2023 Impact Factor: 3.3
2023 SCImago Journal Rankings: 1.188

 

DC FieldValueLanguage
dc.contributor.authorLin, Zhiyang-
dc.contributor.authorZhang, Peng-
dc.contributor.authorGuo, Mingmin-
dc.contributor.authorLyu, Yupei-
dc.contributor.authorJiang, Rui-
dc.contributor.authorWong, SC-
dc.contributor.authorZhang, Xiaoning-
dc.date.accessioned2024-05-08T02:53:00Z-
dc.date.available2024-05-08T02:53:00Z-
dc.date.issued2024-04-19-
dc.identifier.citationTransportmetrica B: Transport Dynamics, 2024, v. 12, n. 1-
dc.identifier.issn2168-0566-
dc.identifier.urihttp://hdl.handle.net/10722/342965-
dc.description.abstract<p>This paper describes the systematical study of a steady-state solution to the Lighthill-Witham-Richards (LWR) model on a single origin-destination parallel road network, in which the user-equilibrium condition is satisfied and shocks on links are permitted. This study derives a novel static traffic assignment model considering the complete fundamental diagram, including the congested branch. For a composite links unit that includes a set of parallel links between two junctions, the user-equilibrium condition is discussed in detail and thus, the so-called user-equilibrium curves are defined. For a single origin-destination parallel road network, we note that shock structures must be introduced to guarantee the existence of the solution when a bottleneck exists, and thus we establish the correlation between the total number of vehicles and the steady-state solution. Moreover, the uniqueness of the solution is proved by introducing priority coefficients when shocks appear. We analytically give the complete solving procedure of the steady-state solution and thus, avoid the iterative algorithms used in other static traffic assignment models. A numerical scheme of the LWR network model is designed to converge the traffic flow into the discussed steady-state solution, by determining the percentages and priority coefficients at junctions. A numerical example is given to validate the convergence for the designed numerical scheme on a road network with two 2×22×2 junctions.<br></p>-
dc.languageeng-
dc.publisherTaylor and Francis Group-
dc.relation.ispartofTransportmetrica B: Transport Dynamics-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectbottleneck effects-
dc.subjectcomposite links unit-
dc.subjectShock discontinuities-
dc.subjectstatic traffic assignment-
dc.subjectuser-equilibrium conditions-
dc.titleSteady-state solution to the LWR model on a single origin-destination parallel road network-
dc.typeArticle-
dc.description.naturepreprint-
dc.identifier.doi10.1080/21680566.2024.2341012-
dc.identifier.scopuseid_2-s2.0-85190830373-
dc.identifier.volume12-
dc.identifier.issue1-
dc.identifier.eissn2168-0582-
dc.identifier.issnl2168-0566-

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