An interconnect within an integrated circuit provides arbitration to select one of a plurality of signal inputs for connection to a signal output. The arbitration applied uses a first arbitration parameter value, in the form of a time stamp value, and, if two or more signal inputs share such a time stamp value, then uses a second arbitration parameter, in the form of a least recently granted value. The time increment applied to the time stamp value associated with each signal input when it is granted access to the signal output is selected to reflect the quality of service to be associated with that signal input. When a comparison is made between time stamp values, the lowest time stamp value is given priority. A large time increment value corresponds to a low priority (quality of service).