Related papers: Kink Solution in a Fluid Model of Traffic Flows

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…

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…

The recent study by Klingenberg, Oberlack & Pluemacher (2020) proposes a new strategy for modeling turbulence in general. A proof-of-concept is presented therein for the particular flow configuration of a spatially evolving turbulent planar…

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…

We prove the existence of multi-soliton and kink-multi-soliton solutions of the Euler-Korteweg system in dimension one. Such solutions behaves asymptotically in time like several traveling waves far away from each other. A kink is 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…

Merging junctions are important network bottlenecks, and a better understanding of merging traffic dynamics has both theoretical and practical implications. In this paper, we present continuous kinematic wave models of merging traffic flow…

In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative…

The aim of this paper is to show the existence of $\mathcal{R}$-bounded solution operator families for a generalized resolvent problem on the half-space arising from a compressible fluid model of Korteweg type. Such a compressible fluid…

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…

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster…

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the…

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we first introduce a continuous multi-commodity kinematic wave…

This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date…

This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…

We investigate steady state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady…

We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…

Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…