Each switch of the data network includes a number of switch ingress ports for receiving arrival data flow. An aggregate flow monitor is operatively associated with each ingress port for monitoring the aggregate arrival data flow in defined traffic constraint envelopes containing frames. An eligibility time computation mechanism computes an eligibility time at which arriving frames to an ingress port will be conformant to the defined traffic envelope to the ingress port given past frame arrivals. A holding mechanism holds the arriving frames to the ingress port until the eligibility time is reached. A release mechanism releases the arriving frames for forwarding at the eligibility time. The aggregate flow monitor, the eligibility time computation mechanism, the holding mechanism, and the release mechanism cooperate to provide an aggregate traffic shaping function, thus allowing the switch to enforce the traffic constraint envelope for each ingress port.