1. A system for arbitrating among N competing entities, each entity operating to generate a service request, said system comprising: a tree structure having (N−1) arbiter nodes organized into K levels, where N&equals;2 K and said levels are designated Level-1 through Level-K; each Level-1 arbiter node operating to select between two competing service requests, and at least one arbiter node at a higher level, designated as a Level-i node, is operable to select between two competing outputs generated by two lower level arbiter nodes (designated as Level-(i−1) nodes) coupled thereto, said competing service requests and said competing outputs being collectively referred to as competing links; each arbiter node having a direction indicator associated therewith, said direction indicator for indicating a particular link that said each arbiter node will pick out of a pair of competing links; and a logic structure for determining a probability value associated with said direction indicator based on a set of predetermined factors relating to said pair of competing links.