471 RWTH Publication No: 707328        2017        IGPM471.pdf
TITLE Macroscopic modeling of multi-lane motorways using a two-dimensional second-order model of traffic flow
AUTHORS Michael Herty, Salissou Moutari, Giuseppe Visconti
ABSTRACT Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one dimensional framework, henceforth lane changing behavior is somehow neglected. In this paper, we propose a macroscopic model, which accounts for lane-changing behavior on motorway, based on a two-dimensional extension of the Aw and Rascle [4] and Zhang [19] macroscopic model for traffic flow. Under conditions, when lane changing maneuvers are no longer possible, the model "relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same approach as in [3], we derive the two-dimensional macroscopic model through scaling of time discretization of a microscopic follow-the-leader model with driving direction. We provide a detailed analysis of the space-time discretization of the proposed macroscopic as well as an approximation of the solution to the associated Riemann problem. Furthermore, we illustrate some features of the proposed model through some numerical experiments.
KEYWORDS traffic flow, macroscopic model, two dimensional model, second-order traffic flow models
DOI 10.1137/17m1151821
78(4), 2252–2278, 2018