A transaction routing device (e.g. an interconnect) for routing transactions in an integrated circuit includes arbitration circuitry for performing arbitration between a plurality of candidate transactions using attribute values associated with the candidate transactions. Candidate transactions are selected for routing to a destination device in dependence on the arbitration. In a cycle in which a new candidate transaction is received, the arbitration is performed using a default attribute value as the attribute value for the new transaction. Meanwhile, the actual attribute value is stored to an attribute storage unit. In a following processing cycle, if the new candidate transaction has not yet been selected for muting, then the arbitration is performed using the actual attribute value stored in the storage unit.