Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result

International audienceWe consider a strongly coupled PDE-ODE system that describes the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle is given by an ODE depending on the downstream traffic density. The moving constraint is expressed by an inequality on the flux, which models the bottleneck created in the road by the presence of the slower vehicle. We prove the existence of solutions to the Cauchy problem for initial data of bounded variation

A numerical scheme for moving bottlenecks in traffic flow

International audienceWe consider a strongly coupled PDE-ODE system that describes the moving bottlenecks created by several buses on a road. The model consists of a scalar conservation law modeling the main traffic evolution and a series of ODEs accounting for the trajectories of the buses, which depend on the surrounding traffic density. The moving bottlenecks are expressed by inequality constraints on the flux. We generalize a conservative finite volume scheme for the constrained hyperbolic PDE using a reconstruction technique and a tracking algorithm for the ODEs. Numerical simulations illustrate the impact of the buses on traffic flow. This is joint work with C. Chalons (Université of Versailles Saint-Quentin, France)

Scalar conservation laws with moving density constraints arising in traffic flow modeling

We prove the existence of solutions of a coupled PDE-ODE system modeling the interaction of a large slow moving vehicle with the surrounding traffic flow. The model consists in a scalar conservation law with moving density constraint describing traffic evolution coupled with an ODE for the slow vehicle trajectory. The constraint location moves due to the surrounding traffic conditions, which in turn are affected by the presence of the slower vehicle, thus resulting in a strong non-trivial coupling

A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow

International audienceIn this paper we introduce a numerical method for tracking a bus trajectory on a road network. The mathematical model taken into consideration is a strongly coupled PDE-ODE system: the PDE is a scalar hyperbolic conservation law describing the traffic flow while the ODE, that describes the bus trajectory, needs to be intended in a Carathéodory sense. The moving constraint is given by an inequality on the flux which accounts for the bottleneck created by the bus on the road. The finite volume algorithm uses a locally non-uniform moving mesh which tracks the bus position. Some numerical tests are shown to describe the behavior of the solution

Stability estimates for scalar conservation laws with moving flux constraints

International audienceWe study well-posedness of scalar conservation laws with moving flux constraints. In particular, we show the Lipschitz continuous dependence of BV solutions with respect to the initial data and the constraint trajectory. Applications to traffic flow theory are detailed

A numerical scheme for moving bottlenecks in traffic flow

International audienceWe consider a strongly coupled PDE-ODE system that describes the moving bottlenecks created by several buses on a road. The model consists of a scalar conservation law modeling the main traffic evolution and a series of ODEs accounting for the trajectories of the buses, which depend on the surrounding traffic density. The moving bottlenecks are expressed by inequality constraints on the flux. We generalize a conservative finite volume scheme for the constrained hyperbolic PDE using a reconstruction technique and a tracking algorithm for the ODEs. Numerical simulations illustrate the impact of the buses on traffic flow. This is joint work with C. Chalons (Université of Versailles Saint-Quentin, France)

Robust tracking control design for fluid traffic dynamics

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DATASAFE: understanding Data Accidents for TrAffic SAFEty Acknowledgments

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Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks

Macroscopic traffic flow optimization on roundabouts

The aim of this paper is to propose an optimization strategy for traffic flow on roundabouts using a macroscopic approach. The roundabout is modeled as a sequence of 2 × 2 with one mainline and secondary incoming and outgoing roads. We consider two cost the total travel time and the total waiting time, which give an estimate of the time by drivers on the network section. These cost functionals are minimized with respect to the of way parameter of the incoming roads. For each cost functional, the analytical expression given for each junction