A printing system capable of processing a plurality of job streams and sub-jobs within a job stream. The system including one or more marking engines, a hopper, and one or more print media destinations. The system further provides a jobs scheduler for determining a schedule for processing queued print sub-jobs of a job stream using a utility function based on dwell time and a system model indicative of the plurality of interconnected processing units. The plurality of sub-jobs employing one or more of the plurality of sheet processing paths including at least one pre-print batch and at least one direct print batch. A sheet itineraries processor is provided for causing the plurality of interconnected processing units to concurrently move sheets of the concurrent sub-jobs along selected sheet processing paths to process the sheets and to deliver the at least one pre-print batch to the hopper and to deliver the at least one direct print batch to the destination.