A method and apparatus for selecting a queue for service across a shared link. The method includes determining a priority for each queue (202) within a plurality of ingresses (102), wherein the priority is instantaneous for a given timeslot for data transfer, selecting a queue having a first priority for each group of queues within each ingress (104) having packets destined for a particular egress (104), selecting a queue having a second priority for each subset of queues having first priorities and having packets destined for the particular egress (104), and selecting the queue having the second priority for service across the shared link in the given timeslot.