On the micro-to-macro limit for first-order traffic flow models on networks

E Cristiani, S Sahu - arXiv preprint arXiv:1505.01372, 2015 - arxiv.org
Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic
flow models are already well understood in the case of vehicles moving on a single road …

Inverting the fundamental diagram and forecasting boundary conditions: How machine learning can improve macroscopic models for traffic flow

M Briani, E Cristiani, E Onofri - Advances in Computational Mathematics, 2024 - Springer
In this paper, we develop new methods to join machine learning techniques and
macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is …

Transport of measures on networks

F Camilli, R De Maio, A Tosin - arXiv preprint arXiv:1610.00512, 2016 - arxiv.org
In this paper we formulate a theory of measure-valued linear transport equations on
networks. The building block of our approach is the initial/boundary-value problem for the …

An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study

M Briani, E Cristiani - arXiv preprint arXiv:1401.1651, 2014 - arxiv.org
In this paper we study a model for traffic flow on networks based on a hyperbolic system of
conservation laws with discontinuous flux. Each equation describes the density evolution of …

A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

E Cristiani, FS Priuli - arXiv preprint arXiv:1409.0350, 2014 - arxiv.org
In this paper we propose a LWR-like model for traffic flow on networks which allows one to
track several groups of drivers, each of them being characterized only by their destination in …

Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road

G Bretti, E Cristiani, C Lattanzio, A Maurizi… - arXiv preprint arXiv …, 2018 - arxiv.org
In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system
which models a slow vehicle (bottleneck) moving on a road together with other cars. The …

An interface-free multi-scale multi-order model for traffic flow

E Cristiani, E Iacomini - arXiv preprint arXiv:1805.08668, 2018 - arxiv.org
In this paper we present a new kind of model for traffic flow which couples a first-order
macroscopic approach with a second-order microscopic approach, avoiding any interface or …

Macroscopic and multi-scale models for multi-class vehicular dynamics with uneven space occupancy: a case study

M Briani, E Cristiani, P Ranut - Axioms, 2021 - mdpi.com
In this paper, we propose two models describing the dynamics of heavy and light vehicles
on a road network, taking into account the interactions between the two classes. The models …

On a degenerate second order traffic model: existence of discrete evolutions, deterministic many-particle limit and first order approximation

D Mazzoleni, E Radici, F Riva - arXiv preprint arXiv:2404.09834, 2024 - arxiv.org
We propose and analyse a new microscopic second order Follow-the-Leader type scheme
to describe traffic flows. The main novelty of this model consists in multiplying the second …

Homogenization of a discrete model for a bifurcation and application to traffic flow

N Forcadel, W Salazar - Journal de Mathématiques Pures et Appliquées, 2020 - Elsevier
The goal of this paper is to derive rigorously a macroscopic traffic flow model, for a simple
bifurcation, from a microscopic model. At the microscopic scale, we consider a first order …