Parking is one of the main elements of sustainable mobility policies, with important implications on traffic congestion and the urban landscape. Self-automated parking lots have the potential to revolutionize parking by reducing by half the space occupied per vehicle. We explore the solution space of parking management strategies with and without system knowledge (i.e. exit time) for self-automated parking lots. Through a large-scale empirical evaluation study, we conclude that the implementation of the system implies (i) a bounded number of in-park movements, (ii) bounded and similar travel distances and (iii) small vehicle removal times. Having knowledge of the exit time allows to considerably improve the performance of the automated parking system.