Section: New Results

Macroscopic traffic flow models on networks

Participants : Guillaume Costeseque, Nikodem Dymski, Paola Goatin, Nicolas Laurent-Brouty, Giulia Piacentini, Florent Berthelin [COFFEE, Inria] , Antonella Ferrara [U Pavia, Italy] , Simone Göttlich [U Mannheim, Germany] , Oliver Kolb [U Mannheim, Germany] .

In  [38], we propose a new mathematical model accounting for the boundedness of traffic acceleration at a macroscopic scale. Our model is built on a first order macroscopic PDE model coupled with an ODE describing the trajectory of the leader of a platoon accelerating at a given constant rate. We use Wave Front Tracking techniques to construct approximate solutions to the Initial Value Problem. We present some numerical examples including the case of successive traffic signals on an arterial road and we compare the solution to our model with the solution given by the classical LWR equation in order to evaluate the impact of bounded acceleration.

The internship of Giulia Piacentini focused on traffic control via moving bottleneck of coordinated vehicles  [35]. The possibility of properly controlling a moving bottleneck to improve the traffic flow was considered. The traffic is represented by means of a macroscopic model able to take into account the interactions with the bottleneck. This latter interacts with the surrounding flow modifying the traffic density and the flow speed profiles. An optimal control problem is stated by using the speed of the moving bottleneck as control variable. Specifically in this paper the MPC (Model Predictive Control) approach is used in order to get a fuel consumption reduction when the traffic is congested due to the presence of a fixed bottleneck on the highway. In addition we have demonstrated that no increase of the travel time is caused by the control application. The concept illustrated in this paper suggests a future innovative traffic control approach. Indeed the prospective of exploiting special vehicles with manipulable speed to control the traffic flow is particularly attractive given the expected increasing penetration rate of autonomous vehicles in traffic networks in future years.

In collaboration with S. Göttlich and O. Kolb, we studied macroscopic traffic flow models on a road network  [36]. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws. These coupling conditions conserve both the number of vehicles and the composition of traffic through the junction. The proposed Riemann solver is based on assignment coefficients, multi-objective optimization of fluxes and priority parameters. We prove that this Riemann solver is well posed in the case of special junctions, including 1-to-2 diverge and 2-to-1 merge.

In the setting of Florent Berthelin's secondement, we rigorously proved the convergence of the micro-macro limit for particle approximations of the Aw-Rascle-Zhang equations with a maximal density constraint  [4]. The lack of BV bounds on the density variable is supplied by a compensated compactness argument.