An apparatus is provided that includes switching circuitry having a plurality of source ports and a plurality of destination ports. The apparatus also includes arbitration circuitry for performing an arbitration operation on a plurality of requests presented at the plurality of source ports in order to determine, for at least one of the destination ports, one of the requests to be output from that destination port. The arbitration operation comprises applying a first arbitration policy in respect of requests presented by a first subset of the plurality of source ports, and a second arbitration policy in respect of requests presented by the plurality of source ports. The first arbitration policy is to reduce head-of-line blocking compared to the second arbitration policy. Consequently, it is possible to reduce head-of-line blocking while reducing the latency for delay intolerant requests presented at some of the source ports.