1. A method for scheduling a crossbar using distributed request-grant-accept arbitration between input group arbiters and output group arbiters in a switch unit, the method comprising: receiving, at an output group arbiter communicably coupled to an output link group comprising a plurality of output links of the switch unit, an indication that the output link group has won an arbitration slot, wherein multiple output links of the output link group are candidates able to satisfy the arbitration slot, and wherein the received indication comprises an indication that the output link group has won the arbitration slot in a grant phase of request-grant-accept arbitration; and during the grant phase of the request-grant-accept arbitration: determining a first output link identifier having a highest priority within an ordered queue among output link identifiers in the ordered queue matching the candidates able to satisfy the arbitration slot, selecting a first output link of the output link group corresponding to the first output link identifier to satisfy the arbitration slot and issue a grant, and updating, by operation of one or more computer processors, the ordered queue based on the selected first output link, wherein the first output link identifier is moved to a bottom of the ordered queue.