This paper presents control formulations which integrate safety indicators as time headway and time to collision in the context of autonomous overtaking. Simulations via a traffic scenario in the high fidelity vehicle simulator IPG CarMaker are used to confirm the validity of the method. Some simple considerations allow to highlight the differences, in particular the time headway formulation is better suitable to guarantee safety in the case of very strong unexpected deceleration of preceding vehicles, while the time to collision approach precedes to similar safety for normal up to high deceleration of the other traffic participants, while offering much better comfort and fuel efficiency. Time headway precedes also to larger inter-vehicle distances, which represent a possible drawback in terms of capacity of the roads but may also make the approach useless in practice, as other drivers may enter into this space and thus remove the advantages of the time headway approach. As a conclusion, a combination of both approaches is suggested.