Fairness in network optimal flow control: optimality of product forms

Consideration is given to the problem of optimal flow control in a multiclass telecommunications environment where each user (or class) desires to optimize its performance while being fair to the other users (classes). The Nash (1950) arbitration scheme from game theory is shown to be a suitable candidate for a fair, optimal operation point in the sense that it satisfies certain axioms of fairness and is pareto optimal. This strategy can be realized by defining the product of individuals user performance objectives as the network optimization criterion. This provides the rationale for considering the product of user powers, as has been suggested in the literature. For delay constrained traffic, the constrained optimization problem of maximizing the product of user throughputs subject to the constraints leads to a Nash arbitration point. It is shown that these points are unique in throughput space, and the authors also obtain some convexity properties for power and delays with respect to throughputs in a Jackson network