47 research outputs found
The Aw-Rascle traffic model with locally constrained flow
We consider solutions of the Aw-Rascle model for traffic flow fulfilling a
constraint on the flux at . Two different kinds of solutions are proposed:
at the first one conserves both the number of vehicles and the
generalized momentum, while the second one conserves only the number of cars.
We study the invariant domains for these solutions and we compare the two
Riemann solvers in terms of total variation of relevant quantities. Finally we
construct ad hoc finite volume numerical schemes to compute these solutions.Comment: 24 page
Lagrangian GSOM traffic flow models on junctions
International audienceThis paper is concerned with the macroscopic modeling and simulation of traffic flow on junctions. More precisely, we deal with a generic class of second order models, known in the literature as the GSOM family. While classical approaches focus on the Eulerian point-of-view, here we recast the model using its Lagrangian coordinates and we treat the junction as a specific discontinuity in Lagrangian framework. We propose a complete numerical methodology based on a finite difference scheme for solving such a model and we provide a numerical example
Multiscale control of generic second order traffic models by driver-assist vehicles
We study the derivation of generic high order macroscopic traffic models from
a follow-the-leader particle description via a kinetic approach. First, we
recover a third order traffic model as the hydrodynamic limit of an Enskog-type
kinetic equation. Next, we introduce in the vehicle interactions a binary
control modelling the automatic feedback provided by driver-assist vehicles and
we upscale such a new particle description by means of another Enskog-based
hydrodynamic limit. The resulting macroscopic model is now a Generic Second
Order Model (GSOM), which contains in turn a control term inherited from the
microscopic interactions. We show that such a control may be chosen so as to
optimise global traffic trends, such as the vehicle flux or the road
congestion, constrained by the GSOM dynamics. By means of numerical
simulations, we investigate the effect of this control hierarchy in some
specific case studies, which exemplify the multiscale path from the
vehicle-wise implementation of a driver-assist control to its optimal
hydrodynamic design.Comment: 22 pages, 3 figure
How can macroscopic models reveal self-organization in traffic flow?
In this paper we propose a new modeling technique for vehicular traffic flow,
designed for capturing at a macroscopic level some effects, due to the
microscopic granularity of the flow of cars, which would be lost with a purely
continuous approach. The starting point is a multiscale method for pedestrian
modeling, recently introduced in Cristiani et al., Multiscale Model. Simul.,
2011, in which measure-theoretic tools are used to manage the microscopic and
the macroscopic scales under a unique framework. In the resulting coupled model
the two scales coexist and share information, in the sense that the same system
is simultaneously described from both a discrete (microscopic) and a continuous
(macroscopic) perspective. This way it is possible to perform numerical
simulations in which the single trajectories and the average density of the
moving agents affect each other. Such a method is here revisited in order to
deal with multi-population traffic flow on networks. For illustrative purposes,
we focus on the simple case of the intersection of two roads. By exploiting one
of the main features of the multiscale method, namely its
dimension-independence, we treat one-dimensional roads and two-dimensional
junctions in a natural way, without referring to classical network theory.
Furthermore, thanks to the coupling between the microscopic and the macroscopic
scales, we model the continuous flow of cars without losing the right amount of
granularity, which characterizes the real physical system and triggers
self-organization effects, such as, for example, the oscillatory patterns
visible at jammed uncontrolled crossroads.Comment: 7 pages, 7 figure