43 research outputs found
The Godunov Method for a 2-Phase Model
We consider the Godunov numerical method to the phase-transition traffic
model, proposed in [6], by Colombo, Marcellini, and Rascle. Numerical tests are
shown to prove the validity of the method. Moreover we highlight the
differences between such model and the one proposed in [1], by Blandin, Work,
Goatin, Piccoli, and Bayen.Comment: 13 page
Fundamental diagrams for kinetic equations of traffic flow
In this paper we investigate the ability of some recently introduced discrete
kinetic models of vehicular traffic to catch, in their large time behavior,
typical features of theoretical fundamental diagrams. Specifically, we address
the so-called "spatially homogeneous problem" and, in the representative case
of an exploratory model, we study the qualitative properties of its solutions
for a generic number of discrete microstates. This includes, in particular,
asymptotic trends and equilibria, whence fundamental diagrams originate.Comment: 14 page
A Riemann solver at a junction compatible with a homogenization limit
We consider a junction regulated by a traffic lights, with n incoming roads
and only one outgoing road. On each road the Phase Transition traffic model,
proposed in [6], describes the evolution of car traffic. Such model is an
extension of the classic Lighthill-Whitham-Richards one, obtained by assuming
that different drivers may have different maximal speed. By sending to infinity
the number of cycles of the traffic lights, we obtain a justification of the
Riemann solver introduced in [9] and in particular of the rule for determining
the maximal speed in the outgoing road.Comment: 19 page
A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
In the present paper a review and numerical comparison of a special class of
multi-phase traffic theories based on microscopic, kinetic and macroscopic
traffic models is given. Macroscopic traffic equations with multi-valued
fundamental diagrams are derived from different microscopic and kinetic models.
Numerical experiments show similarities and differences of the models, in
particular, for the appearance and structure of stop and go waves for highway
traffic in dense situations. For all models, but one, phase transitions can
appear near bottlenecks depending on the local density and velocity of the
flow
A Riemann solver at a junction compatible with a homogenization limit
We consider a junction regulated by a traffic lights, with n incoming roads
and only one outgoing road. On each road the Phase Transition traffic model,
proposed in [6], describes the evolution of car traffic. Such model is an
extension of the classic Lighthill-Whitham-Richards one, obtained by assuming
that different drivers may have different maximal speed. By sending to infinity
the number of cycles of the traffic lights, we obtain a justification of the
Riemann solver introduced in [9] and in particular of the rule for determining
the maximal speed in the outgoing road.Comment: 19 page
From traffic and pedestrian follow-the-leader models with reaction time to first order convection-diffusion flow models
In this work, we derive first order continuum traffic flow models from a
microscopic delayed follow-the-leader model. Those are applicable in the
context of vehicular traffic flow as well as pedestrian traffic flow. The
microscopic model is based on an optimal velocity function and a reaction time
parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian
coordinates result in first order convection-diffusion equations. More
precisely, the convection is described by the optimal velocity while the
diffusion term depends on the reaction time. A linear stability analysis for
homogeneous solutions of both continuous and discrete models are provided. The
conditions match the ones of the car-following model for specific values of the
space discretization. The behavior of the novel model is illustrated thanks to
numerical simulations. Transitions to collision-free self-sustained stop-and-go
dynamics are obtained if the reaction time is sufficiently large. The results
show that the dynamics of the microscopic model can be well captured by the
macroscopic equations. For non--zero reaction times we observe a scattered
fundamental diagram. The scattering width is compared to real pedestrian and
road traffic data
Noise-Induced Stop-and-Go Dynamics in Pedestrian Single-file Motion
Stop-and-go waves are a common feature of vehicular traffic and have also been observed in pedestrian flows. Usually the occurrence of this self-organization phenomenon is related to an inertia mechanism. It requires fine-tuning of the parameters and is described by instability and phase transitions. Here, we present a novel explanation for stop-and-go waves in pedestrian dynamics based on stochastic effects. By introducing coloured noise in a stable microscopic inertia-free (i.e. first order) model, pedestrian stop-and-go behaviour can be described realistically without requirement of instability and phase transition. We compare simulation results to empirical pedestrian trajectories and discuss plausible values for the model’s parameters
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