  Connected automated vehicles have shown great potential to improve the
efficiency of transportation systems in terms of passenger comfort, fuel
economy, stability of driving behavior and mitigation of traffic congestions.
Yet, to deploy these vehicles and leverage their benefits, the underlying
algorithms must ensure their safe operation. In this paper, we address the
safety of connected cruise control strategies for longitudinal car following
using control barrier function (CBF) theory. In particular, we consider various
safety measures such as minimum distance, time headway and time to conflict,
and provide a formal analysis of these measures through the lens of CBFs.
Additionally, motivated by how stability charts facilitate stable controller
design, we derive safety charts for existing connected cruise controllers to
identify safe choices of controller parameters. Finally, we combine the
analysis of safety measures and the corresponding stability charts to
synthesize safety-critical connected cruise controllers using CBFs. We verify
our theoretical results by numerical simulations.
