Methods and apparatus for an ATM network for implementing a fair servicing of all connections during a back-logged condition through the use of a weighted fair queuing technique. The system is particularly suited for systems where the packets/cells are of a fixed size. Although some important approximations are made in the proposed implementation, all of the properties of an ideal weighted fair queuing algorithm are preserved. The sorting methods and apparatus are advantageous in that it is possible to maintain appropriate servicing of connections without sorting all of the individual connections. This may be accomplished by pre-sorting each of the individual virtual circuit connections into a finite number of predetermined bins according to a weight associated with the connection. Thereafter, only the bins need be sorted without having to sort each of the individual connections. Further aspects of the invention include storing the bins in a matrix with an offset value dependent upon the current potential of the bin. In this manner, the overall sorting required to determine the next connection to service is substantially reduced. Accordingly, the invention is suitable for implementations having transmission speeds of multiple gigabits-per-second.