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The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random…

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…

In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized…

This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…

We demonstrate that in Optimal Velocity Model (OVM) delay times of vehicles coming from the dynamical equation of motion of OVM almost explain the order of delay times observed in actual traffic flows without introducing explicit delay…

We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum…

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is…

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…

This study addresses multilane vehicular traffic modelling, focusing on the transition between microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) descriptions. While previous research on multilane traffic has…

In this paper, we consider first order Hamilton-Jacobi (HJ) equations posed on a ``junction'', that is to say the union of a finite number of half-lines with a unique common point. For this continuous HJ problem, we propose a finite…

We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two outgoing roads). At the mesoscopic level, the priority law…

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…

This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established…

Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain…

This paper examines the IDM microscopic car-following model from a dynamical systems perspective, analyzing the effects of delay on congestion formation. Further, a case of mixed-autonomy is considered by controlling one car with…

We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…

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 order term by a nonlinear function of the global density, with…

With the emergence of autonomous vehicles, it is important to understand their impact on the transportation system. However, conventional traffic simulations are time-consuming. In this paper, we introduce an analytical traffic model for…