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 stored priorities associated with the various sources of the information units. A system for allowing peak bursts based on a system of credits and charges is taught along limits on such peak bursts. Also taught is a system for preventing a flow's disconnection and reconnection to the queues from allowing it to unfairly achieve an improved position.