TY - JOUR
T1 - A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times
AU - Bürger , Raimund
AU - Mulet , Pep
AU - Villada , Luis M.
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 728
EP - 758
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.2013.m135
UR - https://global-sci.org/intro/article_detail/aamm/94.html
KW - Traffic flow, multispecies model, anticipation length, reaction time, diffusive correction, quasilinear system of second-order PDEs, stability, numerical simulation.
AB - <p style="text-align: justify;">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.</p>