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 …
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
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 …
macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is …
Transport of measures on networks
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 …
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 …
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 …
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
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 …
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 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 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 …
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 …
bifurcation, from a microscopic model. At the microscopic scale, we consider a first order …