A system and method for efficiently arbitrating traffic on a bus. A computing system includes a fabric for routing traffic among one or more agents and one or more endpoints. The fabric includes multiple arbiters in an arbitration hierarchy. Arbiters store traffic in buffers with each buffer associated with a particular traffic type and a source of the traffic. Arbiters maintain a respective urgency counter for keeping track of a period of time traffic of a particular type is blocked by upstream arbiters. When the block is removed, the traffic of the particular type has priority for selection based on the urgency counter. When arbiters receive feedback from downstream arbiters or sources, the arbiters adjust selection priority accordingly. For example, changes in bandwidth requirement, low latency tolerance and active status cause adjustments in selection priority of stored requests.