Related papers: Conservation laws with a nonlocal flow, Applicatio…
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,…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
Moving bottlenecks, such as slow-driving vehicles, are commonly thought of as impediments to efficient traffic flow. Here, we demonstrate that in certain situations, moving bottlenecks---properly controlled---can actually be beneficial for…
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…
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…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, both in terms of describing the correct "optimal" direction…
We prove the stability of entropy weak solutions of a class of scalar conservation laws with non-local flux arising in traffic modelling. We obtain an estimate of the dependence of the solution with respect to the kernel function, the speed…
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.…
We introduce a new class of nonlocal nonlinear conservation laws in one space dimension that allow for nonlocal interactions over a finite horizon. The proposed model, which we refer to as the nonlocal pair interaction model, inherits at…
In this paper, we investigate the stationary profiles of a convection-diffusion model for unidirectional pedestrian flows in domains with a single entrance and exit. The inflow and outflow conditions at both the entrance and exit as well as…
In vehicular traffic planning it is a long standing problem how to assign demand such on the available model of a road network that an equilibrium with regard to travel time or generalized costs is realized. For pedestrian traffic this…
An extended social force model with a dynamic navigation field is proposed to study bidirectional pedestrian movement. The dynamic navigation field is introduced to describe the desired direction of pedestrian motion resulting from the…
Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general…
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…
This paper introduces a spatially continuous force-based model for simulating pedestrian dynamics. The main intention of this work is the quantitative description of pedestrian movement through bottlenecks and in corridors. Measurements of…
In shared space environments, urban space is shared among different types of road users, who frequently interact with each other to negotiate priority and coordinate their trajectories. Instead of traffic rules, interactions among them are…