A General Microscopic Traffic Model Yielding Dissipative Shocks

Yuri Borisovich Gaididei, Jean Guy Caputo, Peter Leth Christiansen, Jens Juul Rasmussen, Mads Sørensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2016
Volume26
PublisherSpringer
Publication date2018
Pages375-382
ISBN (Print)9783319630823
DOIs
Publication statusPublished - 2018
Event19th European Conference on Mathematics for Industry
- Rúa Lope Gómez de Marzoa, s/n, Campus Vida, Santiago de Compostela, Spain
Duration: 13 Jun 201617 Jun 2016

Conference

Conference19th European Conference on Mathematics for Industry
LocationRúa Lope Gómez de Marzoa, s/n, Campus Vida
CountrySpain
CitySantiago de Compostela
Period13/06/201617/06/2016
SeriesMathematics in Industry
Volume26

Cite this

Gaididei, Y. B., Caputo, J. G., Christiansen, P. L., Rasmussen, J. J., & Sørensen, M. (2018). A General Microscopic Traffic Model Yielding Dissipative Shocks. In Progress in Industrial Mathematics at ECMI 2016 (Vol. 26, pp. 375-382). Springer. Mathematics in Industry, Vol.. 26 https://doi.org/10.1007/978-3-319-63082-3_59
Gaididei, Yuri Borisovich ; Caputo, Jean Guy ; Christiansen, Peter Leth ; Rasmussen, Jens Juul ; Sørensen, Mads. / A General Microscopic Traffic Model Yielding Dissipative Shocks. Progress in Industrial Mathematics at ECMI 2016. Vol. 26 Springer, 2018. pp. 375-382 (Mathematics in Industry, Vol. 26).
@inproceedings{2a99fbcd213942d784495c7a6d9aebf8,
title = "A General Microscopic Traffic Model Yielding Dissipative Shocks",
abstract = "We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.",
author = "Gaididei, {Yuri Borisovich} and Caputo, {Jean Guy} and Christiansen, {Peter Leth} and Rasmussen, {Jens Juul} and Mads S{\o}rensen",
year = "2018",
doi = "10.1007/978-3-319-63082-3_59",
language = "English",
isbn = "9783319630823",
volume = "26",
pages = "375--382",
booktitle = "Progress in Industrial Mathematics at ECMI 2016",
publisher = "Springer",

}

Gaididei, YB, Caputo, JG, Christiansen, PL, Rasmussen, JJ & Sørensen, M 2018, A General Microscopic Traffic Model Yielding Dissipative Shocks. in Progress in Industrial Mathematics at ECMI 2016. vol. 26, Springer, Mathematics in Industry, vol. 26, pp. 375-382, 19th European Conference on Mathematics for Industry
, Santiago de Compostela, Spain, 13/06/2016. https://doi.org/10.1007/978-3-319-63082-3_59

A General Microscopic Traffic Model Yielding Dissipative Shocks. / Gaididei, Yuri Borisovich; Caputo, Jean Guy; Christiansen, Peter Leth; Rasmussen, Jens Juul; Sørensen, Mads.

Progress in Industrial Mathematics at ECMI 2016. Vol. 26 Springer, 2018. p. 375-382 (Mathematics in Industry, Vol. 26).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

TY - GEN

T1 - A General Microscopic Traffic Model Yielding Dissipative Shocks

AU - Gaididei, Yuri Borisovich

AU - Caputo, Jean Guy

AU - Christiansen, Peter Leth

AU - Rasmussen, Jens Juul

AU - Sørensen, Mads

PY - 2018

Y1 - 2018

N2 - We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.

AB - We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.

U2 - 10.1007/978-3-319-63082-3_59

DO - 10.1007/978-3-319-63082-3_59

M3 - Article in proceedings

SN - 9783319630823

VL - 26

SP - 375

EP - 382

BT - Progress in Industrial Mathematics at ECMI 2016

PB - Springer

ER -

Gaididei YB, Caputo JG, Christiansen PL, Rasmussen JJ, Sørensen M. A General Microscopic Traffic Model Yielding Dissipative Shocks. In Progress in Industrial Mathematics at ECMI 2016. Vol. 26. Springer. 2018. p. 375-382. (Mathematics in Industry, Vol. 26). https://doi.org/10.1007/978-3-319-63082-3_59