196,154 research outputs found
Analysis of risk levels for traffic on a multi-lane highway⁎
No full textWe present an analysis of risk levels on multi-lane roads. The aim is to use the crash metrics to understand which direction of the flow mainly influences the safety in traffic flow. In fact, on multi-lane highways interactions among vehicles occur also with lane changing and we show that they strongly affect the level of potential conflicts. In particular, in this study we consider the Time-To-Collision as risk metric and we use the experimental data collected on the A3 German highway
Filtering Methods for Coupled Inverse Problems
No full textIn many applications it is required to determine a parameters set which is suitable for competing models. To this end, we are interested in ensemble methods to solve multiobjective optimization problems. Here, the ensemble Kalman Filter method is applied and adapted in order to solve coupled inverse nonlinear problems using a weighted function approach. An analysis of the mean field limit of the ensemble method yields an explicit update formula for the weights. Numerical examples show the improved performance of the proposed method
Continuous limits for constrained ensemble Kalman filter
No full textThe 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
Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems
No full textIn this paper we are interested in the numerical solution of optimal control problems for non-linear hyperbolic conservation laws. To this aim, we consider relaxation approximations to the conservation laws coupled with the optimal control problem. Following a semi--Lagrangian interpretation of the hyperbolic relaxation system, and its adjoint counterpart, we solve efficiently the time discretization introducing a multi--step scheme in the class of BDF methods. Computational results illustrating the theoretical findings with applications to traffic flow models are presented
Multicommodity flows on road networks
No full textIn this paper, we discuss the multicommodity flow for vehicular traffic on road networks. To model the traffic, we use the "Aw-Rascle" multiclass macroscopic model. We describe a solution to the Riemann problem at junctions with a criterion of maximization of the total flux, taking into account the destination path of the vehicles. At such a junction, the actual distribution depends on the demands and the supplies on the incoming and outgoing roads, respectively. Furthermore, this new distribution scheme captures efficiently key merging characteristics of the traffic and in contrast to M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, leads to an easy computational model to solve approximately the homogenization problem described in M. Herty, S. Moutari and M. Rascle, Networks and Heterogeneous Media, 1, 275-294, 2006, (M. Herty and M. Rascle, SIAM J. Math. Anal., 38(2), 595-616, 2006). Furthermore, we deduce the equivalent distribution scheme for the LWR multiclass model in M. Garavello and B. Piccoli, Commun. Math. Sci., 3, 261-283, 2005, and we compare the results with those obtained with the "Aw-Rascle" multiclass model for the same initial conditions
Discrete-velocity models and relaxation schemes for traffic flows
No full textWe present simple discrete velocity models for traffic flows. The novel
feature in the corresponding relaxation system is the presence of non negative
velocities only. We show that in the small relaxation limit the discrete
models reduce to the Lighthill-Whitham-Richards equation. In addition
we propose second order schemes combined with IMEX time integrators
as proper discretization of the relaxation-type system. Numerical tests
are carried out on various situations in traffic flow. The results show that
the proposed models are capable to describe correctly the formation of
backward waves induced by traffic jam
Derivation and Stability Analysis of a Macroscopic Multilane Model for Traffic Flow
No full textThe mathematical modeling and the stability analysis of multilane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the model is discussed. The proposed numerical tests confirm the theoretical findings between the macroscopic and microscopic modeling, and the results of the stability analysis
Implicit-Explicit Runge : Kutta Schemes for Numerical Discretization of Optimal Control Problems
No full textImplicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge--Kutta methods in the context of optimal control problems.
The analysis of the schemes is based on the continuous optimality system. Using suitable transformations of the adjoint equation, order conditions up to order three are proven as well as the relation between adjoint schemes obtained through different transformations is investigated. Conditions for the IMEX Runge--Kutta methods to be symplectic are also derived. A numerical example illustrating the theoretical properties is presented
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