Related papers: Linearized Theory of Traffic Flow
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 order to develop a toy model for car's traffic in cities, in this paper we analyze, by means of numerical simulations, the transition among fluid regimes and a congested jammed phase of the flow of "kinetically constrained" hard spheres…
Motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in…
In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front…
In Part I of this paper series, several macroscopic traffic model elements for mathematically describing freeway networks equipped with managed lane facilities were proposed. These modeling techniques seek to capture at the macroscopic the…
For the classification of traffic scenes, a description model is necessary that can describe the scene in a uniform way, independent of its domain. A model to describe a traffic scene in a semantic way is described in this paper. The…
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…
The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…
The future motion of traffic participants is inherently uncertain. To plan safely, therefore, an autonomous agent must take into account multiple possible trajectory outcomes and prioritize them. Recently, this problem has been addressed…
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…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
A diffusion's induced transport is defined for a linear model of a Fokker-Plank equation under periodic boundary conditions in one-dimensional geometry. The flow is generated by a diffusion and a periodic deriving force induced by a…
Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797…
Many real life queueing networks have finite buffers with overflows. To understand the behavior of such networks, we consider traffic equations that generalize the traffic equations of classic open queueing networks where some nodes are…
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz…
Scattering through natural porous formations (by far the most ubiquitous example of disordered media) represents a formidable tool to identify effective flow and transport properties. In particular, we are interested here in the scattering…
We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an ($N$+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By…
We introduce a macroscopic model for a network of conveyor belts with various speeds and capacities. In a different way from traffic flow models, the product densities are forced to move with a constant velocity unless they reach a maximal…
We study the urban-scale macroscopic traffic flow in city networks. Star graph is considered as traffic network. Star graphs with controlled traffic flow are transformed to various cell-transmission graphs by using the cell transmission…
This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at…