65 research outputs found
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
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
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
Stability and Optimization in Structured Population Models on Graphs
We prove existence and uniqueness of solutions, continuous dependence from
the initial datum and stability with respect to the boundary condition in a
class of initial--boundary value problems for systems of balance laws. The
particular choice of the boundary condition allows to comprehend models with
very different structures. In particular, we consider a juvenile-adult model,
the problem of the optimal mating ratio and a model for the optimal management
of biological resources. The stability result obtained allows to tackle various
optimal management/control problems, providing sufficient conditions for the
existence of optimal choices/controls.Comment: 22 pages, 7 figure
Polynomial Profits in Renewable Resources Management
A system of renewal equations on a graph provides a framework to describe the
exploitation of a biological resource. In this context, we formulate an optimal
control problem, prove the existence of an optimal control and ensure that the
target cost function is polynomial in the control. In specific situations,
further information about the form of this dependence is obtained. As a
consequence, in some cases the optimal control is proved to be necessarily
bang--bang, in other cases the computations necessary to find the optimal
control are significantly reduced
Autonomous Vehicles Driving Traffic: The Cauchy Problem
This paper deals with the Cauchy Problem for a PDE-ODE model, where a system
of two conservation laws, namely the Two-Phase macroscopic model, is coupled
with an ordinary differential equation describing the trajectory of an
autonomous vehicle (AV), which aims to control the traffic flow. Under suitable
assumptions, we prove a global in time existence result.Comment: 32 page
On the optimization of conservation law models at a junction with inflow and flow distribution controls
The paper proposes a general framework to analyze control problems for
conservation law models on a network. Namely we consider a general class of
junction distribution controls and inflow controls and we establish the
compactness in of a class of flux-traces of solutions. We then derive the
existence of solutions for two optimization problems: (I) the maximization of
an integral functional depending on the flux-traces of solutions evaluated at
points of the incoming and outgoing edges; (II) the minimization of the total
variation of the optimal solutions of problem (I). Finally we provide an
equivalent variational formulation of the min-max problem (II) and we discuss
some numerical simulations for a junction with two incoming and two outgoing
edges.Comment: 29 pages, 14 figure
Differential Equations Modeling Crowd Interactions
Nonlocal conservation laws are used to describe various realistic instances
of crowd behaviors. First, a basic analytic framework is established through an
"ad hoc" well posedness theorem for systems of nonlocal conservation laws in
several space dimensions interacting non locally with a system of ODEs.
Numerical integrations show possible applications to the interaction of
different groups of pedestrians, and also with other "agents".Comment: 26 pages, 5 figure
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