A method and apparatus for scheduling the transmission of cells onto an network, or other packet switching network, is disclosed. The central feature of the scheduling mechanism is a quality of service engine (QoS Engine) which accelerates the processing of packets in a packet switching networks, such as an ATM network, by assisting the accurate pacing of many ATM virtual circuits. The QoS Engine allows the concurrent support of a wide variety of port speeds, traffic classes using different priorities and traffic parameters. quality of service engine (QoS Engine) works in conjunction with a network processor (NP) to allow it to maintain software flexibility, and for it to achieve accurate pacing.