A system for controlling the transmission of cells from a network node over multiple Virtual Circuits (VCs) is disclosed. The system performs traffic shaping, as required by connection based systems such as Asynchronous Transfer Mode (ATM), for each VC connected with a network node, so that the Quality of Service (Qos) parameters established when the connection was established are not exceeded. The system includes a process for scheduling the transmission of cells from the network node. The scheduling process periodically scans a table having entries corresponding to virtual circuits connected with the network node. During each scan of the table, the scheduler increments a sustainable rate accumulator field, a peak rate accumulator field, and a latency accumulator field of each table entry that corresponds with a virtual circuit that is open, and for which there is a cell ready to be transmitted. The scheduler further determines if the sustainable rate accumulator value is greater than or equal to a predetermined value and whether the peak rate accumulator value is greater than or equal to a predetermined value. If both conditions are true, then a cell may be transmitted on the virtual circuit corresponding with that table entry. The system further provides that transmissions are scheduled on virtual circuits having the greatest latency since previous transmissions.