376 research outputs found
A two-dimensional data-driven model for traffic flow on highways
Based on experimental traffic data obtained from German and US highways, we
propose a novel two-dimensional first-order macroscopic traffic flow model. The
goal is to reproduce a detailed description of traffic dynamics for the real
road geometry. In our approach both the dynamic along the road and across the
lanes is continuous. The closure relations, being necessary to complete the
hydrodynamic equation, are obtained by regression on fundamental diagram data.
Comparison with prediction of one-dimensional models shows the improvement in
performance of the novel model.Comment: 27 page
Single- and multi-population kinetic models for vehicular traffic reproducing fundamental diagrams and with low computational complexity.
In this work, we focus on kinetic theory of vehicular traffic. We introduce (Boltzmann and Fokker-Planck) models having the following properties: they are amenable for computations and analytical investigations, but at the same time they are able to characterize and to explain the features of experimental diagrams.
The scattering observed in experimental data is reproduced by a multi-population model. We propose a new interpretation of the dispersion of data since it can be attributed to the heterogeneous composition of the flow. In fact, the scattering is obtained by treating traffic as a mixture of vehicles with different physical and kinematic characteristics.
The multi-population model is built as generalization of a new single-population model for which the analytical expression of the steady state can be computed explicitly. This is possible thanks to the particular choice of the microscopic interactions. These models are able to catch the macroscopic properties of the flow at equilibrium, as the phase transition, the capacity drop and the scattering of data.
The proposed models are endowed with a robust mathematical structure. We study the mathematical properties which induce the structure of diagrams, the well posedness with the existence and uniqueness proof of the solution of the kinetic equations.
A further result of this thesis is the analysis of the effects of the microscopic interactions on the macroscopic dynamics. This purely multiscale issue which is tackled by an asymptotic study of the model in the Fokker-Planck limit
The BGK approximation of kinetic models for traffic
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 deriving a modified formulation of the BGK-type equation.
The new kinetic model allows to reproduce conditionally stable non-equilibrium
phenomena in traffic flow. In particular, stop and go waves appear as bounded
backward propagating signals occurring in bounded regimes of the density where
the model is unstable. The BGK-type model introduced here also offers the
mesoscopic description between the microscopic follow-the-leader model and the
macroscopic Aw-Rascle and Zhang model
Hybrid stochastic kinetic description of two-dimensional traffic dynamics
In this work we present a two-dimensional kinetic traffic model which takes
into account speed changes both when vehicles interact along the road lanes and
when they change lane. Assuming that lane changes are less frequent than
interactions along the same lane and considering that their mathematical
description can be done up to some uncertainty in the model parameters, we
derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the
quasi-invariant interaction limit. By means of suitable numerical methods,
precisely structure preserving and direct Monte Carlo schemes, we use this
equation to compute theoretical speed-density diagrams of traffic both along
and across the lanes, including estimates of the data dispersion, and validate
them against real data
Analysis of a heterogeneous kinetic model for traffic flow
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
interactions, which take place among vehicles belonging to the various classes.
Our approach differs from the multi-population kinetic model based on a lattice
of speeds because here we assume continuous velocity spaces and we introduce a
parameter describing the physical velocity jump performed by a vehicle that
increases its speed after an interaction. The model is discretized in order to
investigate numerically the structure of the resulting fundamental diagrams and
the system of equations is analyzed by studying well posedness. Moreover, we
compute the equilibria of the discretized model and we show that the exact
asymptotic kinetic distributions can be obtained with a small number of
velocities in the grid. Finally, we introduce a new probability law in order to
attenuate the sharp capacity drop occurring in the diagrams of traffic.Comment: 31 page
Continuous Limits for Constrained Ensemble Kalman Filter
The Ensemble Kalman Filter method can be used as an iterative particle
numerical scheme for state dynamics estimation and control--to--observable
identification problems. In applications it may be required to enforce the
solution to satisfy equality constraints on the control space. In this work we
deal with this problem from a constrained optimization point of view, deriving
corresponding optimality conditions. Continuous limits, in time and in the
number of particles, allows us to study properties of the method. We illustrate
the performance of the method by using test inverse problems from the
literature
Industry and Society 10/1974 12 March 1974
Lane changing is one of the most common maneuvers on motorways. Although,
macroscopic traffic models are well known for their suitability to describe
fast moving crowded traffic, most of these models are generally developed in
one dimensional framework, henceforth lane changing behavior is somehow
neglected. In this paper, we propose a macroscopic model, which accounts for
lane-changing behavior on motorway, based on a two-dimensional extension of the
Aw and Rascle [Aw and Rascle, SIAM J.Appl.Math., 2000] and Zhang [Zhang,
Transport.Res.B-Meth., 2002] macroscopic model for traffic flow. Under
conditions, when lane changing maneuvers are no longer possible, the model
"relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same
approach as in [Aw, Klar, Materne and Rascle, SIAM J.Appl.Math., 2002], we
derive the two-dimensional macroscopic model through scaling of time
discretization of a microscopic follow-the-leader model with driving direction.
We provide a detailed analysis of the space-time discretization of the proposed
macroscopic as well as an approximation of the solution to the associated
Riemann problem. Furthermore, we illustrate some features of the proposed model
through some numerical experiments.Comment: 26 page
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