The Optimal Velocity Model (OVM) is a car-following model that captures some interesting real-world phenomena. There are two key variants of this model, which depend on whether they capture the dynamics of a platoon of vehicles travelling on a circular loop, or on an infinitely long road. In this paper, we numerically compare the OVM analysed by Orosz et al.  (which considers a circular loop) and the recently-proposed Modified Optimal Velocity Model (MOVM) (which considers an infinitely long road). A key insight obtained is that the variant with periodic boundary conditions could lead to collisions, which appears to be absent in the MOVM. We also derive a necessary condition for non-oscillatory convergence of the MOVM for autonomous vehicles to avoid oscillatory movements. © 2016 IEEE.