We consider a macroscopic follow-the-leader model of a road traffic. The novelty is that we incorporate the possibility to overtake a slower car. We introduce two ways to simulate overtaking. One is based on swapping initial conditions after the overtaking occurs. Second approach is to formulate the problem as a Filippov system with discontinuous right-hand sides.
@article{702816,
title = {On a traffic problem},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2006},
pages = {37-45},
url = {http://dml.mathdoc.fr/item/702816}
}
Buřič, Lubor; Janovský, Vladimír. On a traffic problem, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2006), pp. 37-45. http://gdmltest.u-ga.fr/item/702816/