Related papers: A hybrid numerical method for a microscopic and ma…
We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…
The traffic modelling often keeps the mesoscopic scale in the theoretical sphere because the integro-differential nature of its equations. In the present work we suggest to use the lattice Boltzmann method to overcome these difficulties. In…
In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…
An extended multi-class Aw-Rascle (AR) model with pressure term described as a function of area occupancy defined in form of proportional densities is presented. Two vehicle classes that is; cars and motorcycles are considered based on an…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
The basic properties of traffic flow are analyzed using a simple deterministic one dimensional "car following model" with continuous variables based on a model introduced by Nagel and Herrmann [Physica A 199 254--269 (1993)] including a few…
Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…
We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill--Whitham--Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models…
In this note, we propose a case study of freeway traffic flow modeled as a hybrid system. We describe two general classes of networks that model flow along a freeway with merging onramps. The admission rate of traffic flow from each onramp…
We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a…
In this paper we extend the Aw-Rascle-Zhang (ARZ) non-equilibrium traffic flow model to take into account the look-ahead capability of connected and autonomous vehicles (CAVs), and the mixed flow dynamics of human driven and autonomous…
Microscopic traffic flow models can be distinguished in lane-based or lane-free depending on the degree of lane-discipline. This distinction holds true only if motorcycles are neglected in lane-based traffic. In cities, as opposed to…
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…
A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area…
We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic…
We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily…