Abstract: A method for scheduling asynchronous transfer mode (ATM) data cells for transmission in an ATM system uses a plurality of queues. The plurality of queues are separated into waiting queues of a lower priority and transmit queues of a higher priority. ATM tokens which identify one active channel a piece are positioned in the queues and rotated/shifted to new positions over time. As time progresses, ATM tokens are shifted/rotated from waiting queues of a lower priority to transfer queues of a higher priority wherein the tokens (and therefore specific ATM channels) are selected and ATM data cell(s) are transmitted in response to the selection. This queued/shifted selection process ensures that bandwidth requirements are adhered to in the ATM system. The selected tokens are eventually (after all needed ATM data cell(s) are transmitted for a single selection) re-scheduled to a queue of lower priority.