  This paper investigates the impact of disturbances on controlling an
autonomous vehicle to smooth mixed traffic flow in a ring road setup. By
exploiting the ring structure of this system, it is shown that velocity
perturbations impacting any vehicle on the ring enter an uncontrollable and
marginally stable mode defined by the sum of relative vehicle spacings. These
disturbances are then integrated up by the system and cannot be unwound via
controlling the autonomous vehicle. In particular, if the velocity disturbances
are zero-mean Gaussians, then the traffic flow on the ring will undergo a
random walk with the variance growing indefinitely and independently of the
control policy applied. In contrast, the impact of acceleration disturbances is
benign as these disturbances do no enter the uncontrollable mode, meaning that
they can be easily regulated using the autonomous vehicle. Our results support
and complement the existing theoretic analysis and field experiments.
