Requests from a plurality of different agents (10) are passed to a request handler via a request concentrator. In front of the request concentrator the requests are queued in a plurality of queues (12). A first one of the agents is configured to issue a priority changing command with a defined position relative to pending requests issued by the first one of the agents (10) to the first one of the queues (12). An arbiter (16), makes successive selections selecting queues (12) from which the request concentrator (14) will pass requests to the request handler (18), based on relative priorities assigned to the queues (12). The arbiter (16) responds to the priority changing command by changing the priority of the first one of the queues (12), selectively for a duration while the pending requests up to the defined position are in the first one of the queues (12). Different queues may be provided for read and write requests from the first one of the agents. In this case, the priority raising request from the agent may be used to raise the priority level of the write queue temporarily to the level of the read queue, until all write requests issued before the priority raising command from the agent have been passed to the request handler.