In this work, we study a group of N homogeneous vehicles travelling on a ring road by describing the collective vehicle dynamics via the so-called Optimal Velocity Model (OVM). We analyze the stability of the equilibrium motion regime in which all vehicles drive at the same speed and keep the same headway. First, stability is studied through linearization, thereby highlighting the roles of the model parameters. Next, we tackle the full nonlinear model and we determine ellipsoidal estimates of the equilibrium's region of attraction by defining and solving suitable Linear Matrix Inequalities (LMIs). Finally, safety aspects are discussed, incorporated in our LMI formulation as lower bounds of the inter-vehicle distances, and illustrated via simulations.