A scheduling mechanism and method for scheduling the output of frames from a plurality of priority queues in a network router or multi-layer switch is disclosed. The method of scheduling packets generally includes the steps of: allocating bandwidth credits for a plurality of queues; dequeuing frames from a current queue if there is available credit; deducting the available credit in accordance with the credit requirements of the frames that are dequeued; and replenishing the available credit for each of the queues when the available credit for the current queue is insufficient to dequeue a frame. Since the available credit for each of the queues is replenished as needed instead of at a regular or periodic interval, the scheduling method is executed independent of time and with reduced computational resources. The present invention offers an efficient variant of deficit round robin, while reducing the computation burden associated with conventional deficit round robin.