Related papers: Kink Solution in a Fluid Model of Traffic Flows
Many car-following models of traffic flow admit the possibility of absolute stability, a situation in which uniform traffic flow at any spacing is linearly stable. Near the threshold of absolute stability, these models can often be reduced…
Based on a study of real traffic data measured on American, UK and German freeways common features of traffic congestion relevant for many transportation engineering applications are revealed by the application of Kerner's three-phase…
We study traffic congestion by analyzing a one dimensional traffic flow model. Developing an asymptotic method to investigate the long time behavior near a critical point, we derive the modified Korteweg-de Vries (mKdV) equation as the…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
The paper examines the model of traffic flow at an intersection introduced in [2], containing a buffer with limited size. As the size of the buffer approach zero, it is proved that the solution of the Riemann problem with buffer converges…
The two phase model for vehicular traffic flows recently appeared in \cite{goatin2006aw} and \cite{BenyahiaRosini01} is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths…
We study traveling wave solutions of the Kerner--Konh\"auser PDE for traffic flow. By a standard change of variables, the problem is reduced to a dynamical system in the plane with three parameters. In a previous paper (Carrillo, F.A., J.…
Given a coercive Hamiltonian which is quasi-convex with respect to the gradient variable and periodic with respect to time and space at least "far away from the origin", we consider the solution of the Cauchy problem of the corresponding…
We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two…
In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…
This study validates the continuum traffic flow model of capacity drop at sag and tunnel bottlenecks, as proposed by Jin (2018) and Wada et al. (2020), through empirical analysis. Specifically, after addressing the limitations in the…
In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density…
Traffic jam in an optimal velocity model with the backward reference function is analyzed. An analytic scaling solution is presented near the critical point of the phase separation. The validity of the solution has been confirmed from the…
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…
We study the spatiotemporal patterns resulting from different boundary conditions for a microscopic traffic model and contrast it with empirical results. By evaluating the time series of local measurements, the local traffic states are…
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…
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…
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…
Extensive research has been conducted to develop statistical and artificial intelligence-based models for predicting short-term crash probabilities using fundamental traffic flow variables and their associated descriptive statistics and…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…