A control device for a compressed air system of a vehicle or for a component of a compressed air system of a vehicle includes at least one processor calculating a prediction of the occurrence and/or duration of overrun condition phases of the vehicle based on altitude position data of a route traveled by or still to be traveled by the vehicle. The control device controls the compressed air system, a component of the compressed air system, or a component intended to operate the compressed air system, based on the calculated prediction.