A General Microscopic Traffic Model Yielding Dissipative Shocks

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

doi:10.1007/978-3-319-63082-3_59

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 proceeding › Article in proceedings › Research › peer-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 language	English
Title of host publication	Progress in Industrial Mathematics at ECMI 2016
Volume	26
Publisher	Springer
Publication date	2018
Pages	375-382
ISBN (Print)	9783319630823
DOIs	https://doi.org/10.1007/978-3-319-63082-3_59
Publication status	Published - 2018
Event	19th European Conference on Mathematics for Industry - Rúa Lope Gómez de Marzoa, Campus Vida, Santiago de Compostela, Spain Duration: 13 Jun 2016 → 17 Jun 2016 Conference number: 19 https://www.usc.gal/congresos/ecmi2016/

Conference

Conference	19th European Conference on Mathematics for Industry
Number	19
Location	Rúa Lope Gómez de Marzoa, Campus Vida
Country/Territory	Spain
City	Santiago de Compostela
Period	13/06/2016 → 17/06/2016
Internet address	https://www.usc.gal/congresos/ecmi2016/

Series	Mathematics in Industry
Volume	26

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

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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",

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booktitle = "Progress in Industrial Mathematics at ECMI 2016",

publisher = "Springer",

note = "19th European Conference on Mathematics for Industry<br/>, ECMI 2016 ; Conference date: 13-06-2016 Through 17-06-2016",

url = "https://www.usc.gal/congresos/ecmi2016/",

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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 et al.
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 proceeding › Article in proceedings › Research › peer-review

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A General Microscopic Traffic Model Yielding Dissipative Shocks

Abstract

Conference

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