A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times
Year: 2013
Author: Raimund Bürger, Pep Mulet, Luis M. Villada
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 728–758
Abstract
Multiclass Lighthill-Whitham-Richards traffic models [Benzoni-Gavage and Colombo, Euro. J. Appl. Math., 14 (2003), pp. 587–612; Wong and Wong, Transp. Res. A, 36 (2002), pp. 827–841] give rise to first-order systems of conservation laws that are hyperbolic under usual conditions, so that their associated Cauchy problems are well-posed. Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws. These terms can be diffusive under certain circumstances, thus, in principle, ensuring the stability of the solutions. The purpose of this paper is to analyze the stability of these diffusively corrected models under varying reaction times and anticipation lengths. It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths, and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m135
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 728–758
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Traffic flow multispecies model anticipation length reaction time diffusive correction quasilinear system of second-order PDEs stability numerical simulation.
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