7 research outputs found
Structural Properties of the Stability of Jamitons
It is known that inhomogeneous second-order macroscopic traffic models can
reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic
condition is violated, uniform traffic flow is unstable, and small
perturbations grow into nonlinear traveling waves, called jamitons. In
contrast, what is essentially unstudied is the question: which jamiton
solutions are dynamically stable? To understand which stop-and-go traffic waves
can arise through the dynamics of the model, this question is critical. This
paper first presents a computational study demonstrating which types of
jamitons do arise dynamically, and which do not. Then, a procedure is presented
that characterizes the stability of jamitons. The study reveals that a critical
component of this analysis is the proper treatment of the perturbations to the
shocks, and of the neighborhood of the sonic points.Comment: 22 page, 6 figure
A statistical mechanics approach to macroscopic limits of car-following traffic dynamics
We study the derivation of macroscopic traffic models from car-following
vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic
description. We consider the superposition of Follow-the-Leader (FTL)
interactions and relaxation towards a traffic-dependent Optimal Velocity (OV)
and we show that the resulting macroscopic models depend on the relative
frequency between these two microscopic processes. If FTL interactions dominate
then one gets an inhomogeneous Aw-Rascle-Zhang model, whose (pseudo) pressure
and stability of the uniform flow are precisely defined by some features of the
microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is
comparable to that of FTL interactions then one gets a
Lighthill-Whitham-Richards model ruled only by the OV function. We further
confirm these findings by means of numerical simulations of the particle system
and the macroscopic models. Unlike other formally analogous results, our
approach builds the macroscopic models as physical limits of particle dynamics
rather than assessing the convergence of microscopic to macroscopic solutions
under suitable numerical discretisations.Comment: 21 pages, 6 figure
A characteristic particle method for traffic flow simulations on highway networks
A characteristic particle method for the simulation of first order
macroscopic traffic models on road networks is presented. The approach is based
on the method "particleclaw", which solves scalar one dimensional hyperbolic
conservations laws exactly, except for a small error right around shocks. The
method is generalized to nonlinear network flows, where particle approximations
on the edges are suitably coupled together at the network nodes. It is
demonstrated in numerical examples that the resulting particle method can
approximate traffic jams accurately, while only devoting a few degrees of
freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth
International Workshop Meshfree Methods for PDE 201
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