  This paper considers the problem of coordinating the vehicular traffic at an
intersection and on the branches leading to it for minimizing a combination of
total travel time and energy consumption. We propose a provably safe
hierarchical-distributed solution to balance computational complexity and
optimality of the system operation. In our design, a central intersection
manager communicates with vehicles heading towards the intersection, groups
them into clusters (termed bubbles) as they appear, and determines an optimal
schedule of passage through the intersection for each bubble. The vehicles in
each bubble receive their schedule and implement local distributed control to
ensure system-wide inter-vehicular safety while respecting speed and
acceleration limits, conforming to the assigned schedule, and seeking to
optimize their individual trajectories. Our analysis rigorously establishes
that the different aspects of the hierarchical design operate in concert and
that the safety guarantees provided by the proposed design are satisfied. We
illustrate its execution in a suite of simulations and compare its performance
to traditional signal-based coordination over a wide range of system
parameters.
