A method for selecting a queue for service across a shared link. The method includes classifying each queue from a group of queues within a plurality of ingresses into one tier of a number “N” of tiers. The number “N” is greater than or equal to 2. Information about allocated bandwidth is used to classify at least some of the queues into the tiers. Each tier is assigned a different priority. The method also includes matching queues to available egresses by matching queues classified within tiers with higher priorities before matching queues classified within tiers with lower priorities.