Related papers: A nonlocal traffic flow model with stochastic velo…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters.…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random…
When a new vehicle joins a lane, those behind may have to temporarily slow to accommodate them. Changing lane can be forced due to lane drops or junctions, but may also take place spontaneously at discretion of drivers, and recent studies…
We continue the development of the theory of pathwise stochastic entropy solutions for scalar conservation laws in $\R^N$ with quasilinear multiplicative ''rough path'' dependence by considering inhomogeneous fluxes and a single rough path…
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 present large scale and detailed analysis of the microscopic empirical data of the traffic flow, focusing on the non-linear interactions between the vehicles when the traffic is congested. By implementing a "renormalisation" procedure…
In this work, we show that the inverse-$\lambda$ shape in the fundamental diagram of traffic flow can be produced dynamically by a simple nonlinear mesoscopic model with stochastic noises. The proposed model is based on the gas-kinetic…
In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…
We present a macroscopic traffic flow model that extends existing fluid-like models by an additional term containing the second derivative of the safe velocity. Two qualitatively different shapes of the safe velocity are explored: a…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
We present a Godunov type numerical scheme for a class of scalar conservation laws with non-local flux arising for example in traffic flow models. The proposed scheme delivers more accurate solutions than the widely used Lax-Friedrichs type…
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential…
We extend our recently introduced stochastic nonlocal traffic flow model to more general random perturbations, including Markovian noise derived from a discretized Jacobi-type stochastic differential equation. Invoking a deterministic…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this…