Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow

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 a one dimensional framework, henceforth lane changing behavior is either not explicitly modeled or explicitly forbidden. 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 [39] 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 model as well as an approximation of the solution to the associated Riemann problem. Furthermore, we illustrate some promising features of the proposed model through some numerical experiments.

Analysis of risk levels for traffic on a multi-lane highway

“…In other words, the inverse of the TTC is able to describe the time evolution of the specific volume and therefore this in turn means that there is a strict link between the safety and the congestion level of the road. This result can be easily extended also to the two-dimensional case, using the considerations introduced in Herty et al (2017b). In addition, the above result paves the way to a possible realtime analysis of the potential conflicts on a road by means of macroscopic models.…”

A two-dimensional data-driven model for traffic flow on highways

“…In fact, it is expected that as in [23] the additional degree of freedom in the modeling allows for a better adjustment of the models to data. Further, in [33] we study a second-order two-dimensional macroscopic model as limit of a two-dimensional microscopic follow-the-leader model which is validated using the German data-set. Instead, in [35] we study a two-dimensional hybrid kinetic model which allows to take into account the two-dimensional phenomena of traffic flow in the kinetic theory showing, as application, that it is able to reproduce the US data-sets.…”

A two-dimensional multi-class traffic flow model

“…The parameters of the test are L = 100 m, ∆x = 0.2 m, T = 4 s, C = 1 in (22), c ρ = 80 and c µ = 0. We use a Godunov scheme [18] to approximate problem (21).…”

“…The most common approaches which include lane-changing are the two-dimensional models and the multi-lane models. The first approach is an emerging topic, and we refer to [6,21,22] for some examples. The second approach has been used for instance in [26,27], where the authors propose a microscopic, a kinetic and a fluid dynamic model with lane changing.…”