Related papers: Analysis and Control of a Non-Local PDE Traffic Fl…
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 characterized by widely different types of vehicles and…
We prove the well-posedness of entropy weak solutions for a class of space-discontinuous scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem adding a viscosity term and we provide $L^\infty$…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
This paper introduces a novel approach to PDE boundary control design using neural operators to alleviate stop-and-go instabilities in congested traffic flow. Our framework leverages neural operators to design control strategies for traffic…
A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…
Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation…
This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and…
This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential…
We investigate a class of nonlocal conservation laws with the nonlinear advection coupling both local and nonlocal mechanism, which arises in several applications such as the collective motion of cells and traffic flows. It is proved that…
Nonlinear dynamics of fluid conveying pipe, rotating with constant velocity about its longitudinal axis is analyzed. Considering boundary conditions and internal damping, the nonlinear equation of motion is derived, and it is discretized…
We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from an origin to a destination as quickly as possible. Flow patterns vary over…
Macroscopic traffic flow models are essential for analysing traffic dynamics in highways and urban roads. While second-order models like METANET capture non-equilibrium traffic states, they often produce unrealistic speed predictions, such…
A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless…
We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…
The Gipps car-following model is a widely used tool for studying and simulation traffic dynamics. Despite its popularity an often disregarded property is that under heterogeneous parametrization on the individual vehicles in the traffic…
In this paper, we study stability properties of solutions to scalar conservation laws with a class of non-convex fluxes. Using the theory of $a$-contraction with shifts, we show $L^2$-stability for shocks among a class of large…
The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is…
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…