Related papers: Kink Solution in a Fluid Model of Traffic Flows
In this article we introduce a new Riemann solver for traffic flow on networks. The Priority Riemann solver (PRS) provides a solution at junctions by taking into consideration priorities for the incoming roads and maximization of through…
We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars…
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…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
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…
We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…
The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or…
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…
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…
Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory…
An analytical framework for turbulent channel flow is developed based on the Alexeev hydrodynamic equations, focusing on the coupled behavior of streamwise and transverse velocity components. The mean streamwise velocity is represented as a…
We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of…
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…
Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop…
We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are…
We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the…
The Simon-Gutowitz bidirectional traffic model (Phys. Rev. E 57, 2441 (1998)) is revisited in this letter. We found that passing cars get stuck with oncoming cars before returning to their home lanes. This provokes the occurrence of wide…
J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost K\"ahler manifolds generalising K\"ahler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-K\"ahler…