A switching method and apparatus operates as a work conserving network device. An arbiter using an arbitration algorithm controls a switch fabric interconnecting input ports and output ports. To switch cells, a virtual output queue of an input port is selected that corresponds to an output port with a lowest occupancy rating and a request is sent to this output port. In a greedy version of the algorithm, input ports may send requests to the lowest occupied output port for which they have a cell. In a non-greedy version, requests may only be sent if that input port has a cell for the lowest occupied output port in the entire network device. An output port that receives one or more requests from input ports uses an input port selection algorithm to select an input port from which to receive a packet. After as many input and output ports are matched as is possible in a phase, the packets for those matched ports are transferred across the switch. The switch fabric operates with a speedup of only twice that of the input port data rates and is still work conserving.