Exchanges between partners in 2015

During the fourth year of the project we had the following research visit exchanges:

1. Maria Laura Delle Monache, Post-Doc at Rutgers University, visited Inria from March 30 to April 4, 2015.
2. Guillaume Costeseque, Post-Doc at Inria, visited UC Berkeley from May 10 to 22 and from October 3 to 10, 2015.

Advances of the work program

During this fourth year, we focused mainly onthe following topics:

• Construction of a general Riemann Solver at junctions
1. We developed a new junction solver that is able to overcome some of the common problems present in existing junction models such as the loss of supply and the blockage of one of the incoming roads by extending the model already developed in the previous three years of the associated team. We further developed a new numerical scheme that allows us to simulate several junctions with multiple incoming and outgoing roads.
2. We are currently developing a soundproof mathematical framework for the new solver. We will work on the theoretical results of the problem, i.e. existence of solutions for general Cauchy problems.


• Lax-Hopf formula for a general Hamilton-Jacobi equation with time and space dependent Hamiltonians
1. We have developed a methodology for the efficient resolution of traffic flow models on a junction, based on Hamilton-Jacobi equations and the so-called variational approach. Our approach conjugates the exactness of the representation formula (or Lax-Hopf formula) outside of the junction point and the inf-morphism property, as well as the notions of supply and demand on a junction.
2. The next steps will be the evaluation of the developed methodology with use of real data collected through the UC Berkeley Connected Corridors project and the exploration of the link between Hamilton-Jacobi equations and conservation laws on a junction, for instance, deriving a Lax-Oleinik formula.

Joint papers resulting from the collaboration

During this year we revised the paper

S.Samaranayake, J. Reilly, W.Krichene, M.L. Delle Monache, P.Goatin, A. Bayen, Discrete-time system optimal dynamic traffic assignment (SO-DTA) with partial control for horizontal queuing networks.

the paper

J. Reilly, S. Samaranayake, M.L. Delle Monache, W. Krichene, P. Goatin and A. Bayen, Adjoint-based optimization on a network of discretized scalar conservation law PDEs with applications to coordinated ramp metering,

has been revised and accepted for publication on Journal of Optimization and Applications theory, and the paper

S.Samaranayake, W.Krichene, J. Reilly, M.L. Delle Monache, J.B. Lespiau, P.Goatin, A. Bayen, Discrete-time system optimal dynamic traffic assignment (SO-DTA) with partial control for horizontal queuing networks.

has been accepted for publications on 2015 American Control Conference, Chicago, IL, 2015, p.663-670.