Related papers: A Kink Soliton Characterizing Traffic Congestion
We found, through analytical and numerical methods, new towers of infinite number of asymptotically conserved charges for deformations of the Korteweg-de Vries equation (KdV). It is shown analytically that the standard KdV also exhibits…
A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of…
Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…
We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents,…
We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion…
The congestion of a motorway section is propagated to its neighbouring sections, leading to correlations. The resulting correlation matrix encodes the information on congestion. Here, we study symmetrized time-lagged correlations and show…
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…
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 consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
We study the existence of weak solutions to the two-phase model of crowd motion. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two…
This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…
This paper examines the effects of a thin layer of inhomogeneity on periodic solutions of the Multiple-sine-Gordon (MsG) model. We investigate the dynamics of the perturbed Double-sine-Gordon (DsG) system as a significant and more practical…
We investigate characteristic properties of the congested traffic states on a 30 km long stretch of the German freeway A5 north of Frankfurt/Main. Among the approximately 245 breakdowns of traffic flow in 165 days, we have identified five…
We review two models of optimal transport, where congestion effects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
Traffic congestion at urban-scale levels occurs when road network supply is insufficient compared with demand. Therefore, the relationship between supply and demand has been extensively investigated in the literature. Especially the impact…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
This paper examines the IDM microscopic car-following model from a dynamical systems perspective, analyzing the effects of delay on congestion formation. Further, a case of mixed-autonomy is considered by controlling one car with…