A method for scheduling a crossbar using distributed request-grant-accept arbitration between input group arbiters and output group arbiters in a switch unit is provided. Each input group arbiter and output group arbiter maintains an ordered queue of links in an input group or an output group. The ordered queue prioritizes links in the output group or output group that was least recently selected. To satisfy an arbitration slot won on the group-level, the input group arbiter or output group arbiter starts a search from the oldest link that was selected and maintains fairness among links in the group.