A stochastic approximation approach for max-min fair adaptive rate control of ABR sessions with MCRs

The ABR sessions in an ATM network share the bandwidth left over after guaranteeing service to CBR and VER traffic. Hence the bandwidth available to ABR sessions is randomly varying. This bandwidth must be shared by the sessions in a max-min fair fashion. Our point of departure in this paper is to formulate the problem of determining the max-min fair session rates as the problem of finding the root of a certain nonlinear vector equation; the same formulation also arises with our notion of max-min fairness with positive MCRs. This formulation allows us to use a stochastic approximation algorithm for online distributed computation of the max-min fair rates. We use the well known ordinary differential equation technique to prove convergence of the algorithm in the synchronous update case. We provide simulation results using the NIST simulator to show that the algorithm is able to track the max-min fair rates for slowly varying random available link bandwidths.