Abstract: A processor unit (3) for model-based predictive control of a vehicle (1) taking into account an arrival time factor is configured to calculate a trajectory for the vehicle (1) based at least in part on at least one arrival time factor, with the trajectory including an entire route (20) to a specified destination (19) at which the vehicle (1) is to arrive, and with the at least one arrival time factor influencing an arrival time of the vehicle (1) at the specified destination (19). Additionally, the processor unit (3) is configured to optimize a section of the trajectory for the vehicle (1) for a sliding prediction horizon by executing a model-based predictive control (MPC) algorithm (13), where the MPC algorithm (13) includes a longitudinal dynamic model (14) of a drive train (7) of the vehicle (1) and a cost function (15) to be minimized.