Related papers: A Space-time Nonlocal Traffic Flow Model: Relaxati…
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
This paper develops boundary control for freeway traffic with a downstream bottleneck. Traffic on a freeway segment with capacity drop at outlet of the segment is a common phenomenon leading to traffic bottleneck problem. The capacity drop…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or "local") conservation law. In this note we overview recent…
We study a message passing model, applicable also to traffic problems. The model is implemented in a discrete lattice, where particles move towards their destination, with fluctuations around the minimal distance path. A repulsive…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…
In this note, we introduce some models of pedestrian traffic and prove existence and uniqueness for these models.
In this paper we model pedestrian flows evacuating a narrow corridor through an exit by a one-dimensional hyperbolic conservation law with a non-local constraint. Existence and stability results for the Cauchy problem with Lipschitz…
Free-flow road networks, such as suburban highways, are increasingly experiencing traffic congestion due to growing commuter inflow and limited infrastructure. Traditional control mechanisms, such as traffic signals or local heuristics, are…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…
In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabola potential, we…
We consider a class of nonlocal conservation laws modeling traffic flows, given by $ \partial_t u_\varepsilon + \partial_x(V(u_\varepsilon \ast \gamma_\varepsilon) u_\varepsilon) = 0$, with a rescaled convolution kernel…
The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models, only repulsive forces and advection terms are taken into…
We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a…
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…