This book explores the development of PDE (partial differential equation) backstepping
controllers for the suppression of stop-and-go instabilities and oscillations in congested …

We introduce a Follow-the-Leader approximation of a nonlocal generalized Aw--Rascle--
Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the …

We consider a system of nonlocal balance laws where each balance law is coupled with the
remaining balance laws both by a nonlocal velocity function that takes into account the …

A detailed symmetry analysis is performed for a microscopic model used to describe traffic
flow in two-lane motorways. The traffic flow theory employed in this model is a two …

We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic
following the traditional Lighthill--Whitham--Richards model where the velocity in each lane …

While macroscopic models for single or multi-lane traffic flow are well established, these
models are not applicable to the dynamics and characteristics of disordered traffic which is …

This paper introduces two macroscopic lane change models, separately for small vehicles
(passenger cars and vans) as well as heavy vehicles. The model is structured using a …

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the
microscopic scale, studying a model based on two interaction terms. To do this we propose …

This article aims to study coupled mean-field equation and ODEs with discrete events
motivated by vehicular traffic flow. Precisely, multi-lane traffic flow in presence of human …

Physical solutions to the widely used Aw–Rascle–Zhang (ARZ) traffic model and the
adapted pressure (AP) ARZ model should satisfy the positivity of density, the minimum and …