A packet scheduler controls dispatch of packets containing constant bit rate (CBR) or real time variable bit rate (rt-VBR) at an ingress operation of multiplexing the packets into payloads of an asynchronous transfer mode (ATM) bearer virtual circuit connection. Packets can be queued in one of a number of queues according to priority. The scheduler controls assembly of common part sublayer payload data units (CPS-PDU) comprising any unused octets from a previous packet partially dispatched, and whole packets in order of priority. If a holdover timer period expires before a common part sublayer payload data unit is completed, the payload of that data unit is packed with null data; and dispatched. The packet dispatch is controlled so as to match the traffic characteristics of an underlying bearer channel.