  A fundamental problem in traffic networks is driving under safety and limited
physical space constraints. In this paper, we design longitudinal vehicle
controllers and study the dynamics of a system of homogeneous vehicles on a
single-lane ring road in order to understand the interplay of limited space,
speed, and safety. Each vehicle in the system either operates in the cruise
control mode or follows a vehicle ahead by keeping a safe time headway. We show
that if the number of vehicles is less than a certain critical threshold,
vehicles can occupy the limited space in many different configurations, i.e.,
different platoons of different sizes, and they converge to a uniform maximum
speed while attenuating errors in the relative spacing upstream a platoon. If
the number of vehicles exceeds the threshold, vehicles converge to a unique
symmetric configuration and the equilibrium speed decreases as the number of
vehicles increases. Next, we consider vehicle-to-vehicle (V2V) communication
and show that it increases the critical number of vehicles that can travel with
the maximum speed. Finally, we consider central coordination and show that the
proposed controllers can force vehicles to converge to a desired configuration
specified by the coordinator while maintaining safety and comfort. We
demonstrate the performance of the proposed controllers via simulation.
