A system and method of moving information units from a network processor toward a data transmission network in a prioritized sequence which accommodates several different levels of service. The present invention includes a method and system for scheduling the egress of processed information units (or frames) from a network processing unit according to service based on minimum bandwidth specifications where position in the queue is adjusted after each service based on minimum bandwidth specificaiton and the length of frame, a process which is subject to rounding errors. To avoid the accumulation of rounding errors inequitably influencing the position of some in the queue, a system to adjust for the rounding errors adds an increased measure of fairness to the system.