Centralized Traffic Control via Small Fleets of Connected and Automated Vehicles

In this paper we propose a model for mixed traffic composed of few Connected and Automated Vehicles (CAVs) in the bulk flow. We rely on a multi-scale approach, coupling a Partial Differential Equation describing the overall traffic flow and Ordinary Differential Equations accounting for CAV trajectories, which act as moving bottlenecks on the surrounding flux. In our framework, CAVs are allowed to overtake (if on different lanes) or merge (if on the same lane). Controlling CAV desired speeds allows to act on the system to minimize any traffic density dependent cost function. More precisely, we apply Model Predictive Control to reduce fuel consumption in congested situations. In particular, we observe how the CAV number impacts the result, showing that low penetration rates are sufficient to significantly improve the selected performance indexes. The outcome of this paper supports the attractive perspective of exploiting a small number of controlled vehicles as endogenous actuators to regulate traffic flow on road networks.