  We consider the problem of scaling up optimal and safe controllers for
Connected and Automated Vehicles (CAVs) from a single Control Zone (CZ) around
a traffic conflict area to an entire network. The goal is to jointly minimize
travel time and energy consumption for all CAVs, while providing
speed-dependent safety guarantees within a CZ and satisfying velocity and
acceleration constraints. A hierarchical modular CZ framework is developed
consisting of a lower level where decentralized controllers are used that
combine Optimal control and Control Barrier Functions (OCBF) and a higher level
where a feedback flow controller is proposed to coordinate adjacent CZs. The
flow controller is parameterized by a terminal velocity constraint that serves
as the interface between CZs. Simulation results show that the proposed modular
control zone framework outperforms a direct extension of the OCBF framework to
multiple CZs without any flow control.
