A min-plus derivation of the fundamental car-traffic law

Autores
Lotito, Pablo Andres; Mancinelli, Elina Mafalda; Quadrat, Jean Pierre
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing thedynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulae we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the  MaxPlus toolbox of Scilab confirm the theoretical results obtained.
Fil: Lotito, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Institut national de recherche sur les transports et leur sécurité; Francia
Fil: Mancinelli, Elina Mafalda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Institut National de Recherche en Informatique et en Automatique; Francia
Fil: Quadrat, Jean Pierre. Institut National de Recherche en Informatique et en Automatique; Francia
Materia
CELLULAR AUTOMATA
FUNDAMENTAL DIAGRAM
LYAPUNOV EXPONENT
MAX-PLUS ALGEBRA
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/239879
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/239879
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A min-plus derivation of the fundamental car-traffic lawLotito, Pablo AndresMancinelli, Elina MafaldaQuadrat, Jean PierreCELLULAR AUTOMATAFUNDAMENTAL DIAGRAMLYAPUNOV EXPONENTMAX-PLUS ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing thedynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulae we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the  MaxPlus toolbox of Scilab confirm the theoretical results obtained.Fil: Lotito, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Institut national de recherche sur les transports et leur sécurité; FranciaFil: Mancinelli, Elina Mafalda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Institut National de Recherche en Informatique et en Automatique; FranciaFil: Quadrat, Jean Pierre. Institut National de Recherche en Informatique et en Automatique; FranciaInstitute of Electrical and Electronics Engineers2005-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/239879Lotito, Pablo Andres; Mancinelli, Elina Mafalda; Quadrat, Jean Pierre; A min-plus derivation of the fundamental car-traffic law; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 50; 5; 5-2005; 699-7050018-9286CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/1431054info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2005.848336info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:48Zoai:ri.conicet.gov.ar:11336/239879instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:54:49.104CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A min-plus derivation of the fundamental car-traffic law
title A min-plus derivation of the fundamental car-traffic law
spellingShingle A min-plus derivation of the fundamental car-traffic law
Lotito, Pablo Andres
CELLULAR AUTOMATA
FUNDAMENTAL DIAGRAM
LYAPUNOV EXPONENT
MAX-PLUS ALGEBRA
title_short A min-plus derivation of the fundamental car-traffic law
title_full A min-plus derivation of the fundamental car-traffic law
title_fullStr A min-plus derivation of the fundamental car-traffic law
title_full_unstemmed A min-plus derivation of the fundamental car-traffic law
title_sort A min-plus derivation of the fundamental car-traffic law
dc.creator.none.fl_str_mv Lotito, Pablo Andres
Mancinelli, Elina Mafalda
Quadrat, Jean Pierre
author Lotito, Pablo Andres
author_facet Lotito, Pablo Andres
Mancinelli, Elina Mafalda
Quadrat, Jean Pierre
author_role author
author2 Mancinelli, Elina Mafalda
Quadrat, Jean Pierre
author2_role author
author
dc.subject.none.fl_str_mv CELLULAR AUTOMATA
FUNDAMENTAL DIAGRAM
LYAPUNOV EXPONENT
MAX-PLUS ALGEBRA
topic CELLULAR AUTOMATA
FUNDAMENTAL DIAGRAM
LYAPUNOV EXPONENT
MAX-PLUS ALGEBRA
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing thedynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulae we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the  MaxPlus toolbox of Scilab confirm the theoretical results obtained.
Fil: Lotito, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Institut national de recherche sur les transports et leur sécurité; Francia
Fil: Mancinelli, Elina Mafalda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Institut National de Recherche en Informatique et en Automatique; Francia
Fil: Quadrat, Jean Pierre. Institut National de Recherche en Informatique et en Automatique; Francia
description We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing thedynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulae we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the  MaxPlus toolbox of Scilab confirm the theoretical results obtained.
publishDate 2005
dc.date.none.fl_str_mv 2005-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/239879
Lotito, Pablo Andres; Mancinelli, Elina Mafalda; Quadrat, Jean Pierre; A min-plus derivation of the fundamental car-traffic law; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 50; 5; 5-2005; 699-705
0018-9286
CONICET Digital
CONICET
url http://hdl.handle.net/11336/239879
identifier_str_mv Lotito, Pablo Andres; Mancinelli, Elina Mafalda; Quadrat, Jean Pierre; A min-plus derivation of the fundamental car-traffic law; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 50; 5; 5-2005; 699-705
0018-9286
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/1431054
info:eu-repo/semantics/altIdentifier/doi/10.1109/TAC.2005.848336
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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