An arbitrator (24) is disclosed for reordering access requests (25) to a memory system (150) to reduce memory system conflicts. The arbitrator comprises a transaction buffer (203) for buffering the access requests (25), an output counter (207) for counting access requests issued by the arbitrator (24), a mapping table (211) for mapping at least the output counter (207) to the access requests (25) in the transaction buffer (203), and a reordering unit (225) for dynamically re-ordering entries in the mapping table (211) such that the mapping points to the access requests (25) in an issue order wherein memory system conflicts are reduced.