A General Microscopic Traffic Model Yielding Dissipative Shocks

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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
Publication date2018
ISBN (Print)9783319630823
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


Conference19th European Conference on Mathematics for Industry
LocationRúa Lope Gómez de Marzoa, s/n, Campus Vida
CitySantiago de Compostela
SeriesMathematics in Industry
CitationsWeb of Science® Times Cited: No match on DOI

ID: 146506263