Private car commuting is heavily dependent on the subsidisation that exists in the form of available free parking. However, the public funding policy of such free parking has been changing over the last years, with a substantial increase of meter-charged parking areas in many cities. To help to increase the sustainability of car transportation, a novel concept of a self-automated parking lot has been recently proposed, which leverages on a collaborative mobility of parked cars to achieve the goal of parking twice as many cars in the same area, as compared to a conventional parking lot. This concept, known as self-automated parking lots, can be improved if a reasonable prediction of the exit time of each car that enters the parking lot is used to try to optimize its initial placement, in order to reduce the mobility necessary to extract blocked cars. In this paper we show that the exit time prediction can be done with a relatively small error, and that this prediction can be used to reduce the collaborative mobility in a self-automated parking lot.