On the modified AIMD algorithm for distributed resource management with saturation of each user's share

Recently the additive increase multiplicative decrease (AIMD) algorithm has been applied in fields other than congestion control in communications networks. A major attribute of these new applications is that the share of each user is bounded. Simulations suggest that AIMD performs well, even in the case of individual constraints on each user. In this paper, we provide a formal proof of exponential convergence to a unique fixed-point for the AIMD algorithm under individual user constraints.