Fairness in network optimal flow control

The authors consider 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 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 individual 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 of computer communication networks. It is shown that these points are unique in the throughput space, and some convexity properties for power and delays respect to throughputs in a Jackson network are also obtained