Related papers: A non-local traffic flow model for 1-to-1 junction…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…
In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends…
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…
Urban intersections are prone to delays and inefficiencies due to static precedence rules and occlusions limiting the view on prioritized traffic. Existing approaches to improve traffic flow, widely known as automatic intersection…
We use the asymmetric simple exclusion process for describing vehicular traffic flow at the intersection of two streets. No traffic lights control the traffic flow. The approaching cars to the intersection point yield to each other to avoid…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
In this paper, a finite volume approximation scheme is used to solve a non-local macroscopic material flow model in two space dimensions, accounting for the presence of boundaries in the non-local terms. Based on a previous result for the…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
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. Analogous connections in the case of road networks are instead…
We propose a microscopic traffic model where the update velocity is determined by the deceleration capacity and response time. It is found that there is a class of collisions that cannot be distinguished by simply comparing the stop…
We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise…
The paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with possible nudging (or "look behind") terms. The obtained conditions are novel, as they are not…
We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the…
We present a macroscopic traffic flow model where standard vehicles coexist with vehicles informed on the traffic distribution. The resulting mixed nonlocal-local integro-differential PDEs is proved to generate a locally Lipschitz…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
In the Biham-Middleton-Levine traffic model cars are placed with some density p on a two dimensional torus, and move according to a (simple) set of predefined rules. Computer simulations show this system exhibits many interesting phenomena:…