An apparatus for performing arbitration increases the fairness of arbitrations, decreases system latency, increases system throughput, and is suitable for use in more complex systems. According to an exemplary embodiment, the apparatus includes a generator for generating a plurality of arbitration numbers corresponding to a plurality of agents, and circuitry for selecting one of the agents to access a resource shared by the agents based on the arbitration numbers. At least one of the arbitration numbers includes a plurality of fields corresponding to a plurality of parameters.