On-ramp simulations and solitary waves of a car-following model

An on-ramp simulation of a car-following model reveals qualitatively similar results to previous simulations of continuum models carried out by Helbing et al. [Phys. Rev. Lett. 82, 4360 (1999)] and by Lee, Lee, and Kim[Phys. Rev. E 59, 5101 (1999)]. Here, we discuss the solitary solution type in greater detail. It can be approximated by a Kortweg-de Vries equation derived from the analogous continuum version. Hence, this establishes a further link between these two traffic simulation types and supports the idea that models of either kind lead to similar results when they contain a relaxation term.