Related papers: Nonlocal reaction traffic flow model with on-off r…
We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…
A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…
We investigate one-dimensional scalar balance laws with singular convolution-type source terms. Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in ${\bf L}^2(\mathbb{R})$,…
Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…
We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average…
We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized…
General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small $BV$ data under appropriate assumptions on the decay of the…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…
In this study, we revisit the spectral transfer model for the turbulent intensity in the passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented.…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…