Fairness and Aggregation: A Primal Decomposition Study

We examine the fair allocation of capacity to a large population of best-effort connections in a typical multiple access communication system supporting some bandwidth on demand processes. Because of stringent limitations on the signalling overhead and time available to transmit and process information, it is not possible to solve the allocation globally to obtain the optimally fair allocation vector. A two-level procedure is proposed where connections are aggregated within terminals, which send aggregated requests to the controller. The controller then computes the appropriate aggregated allocation per terminal and sends the corresponding allocation vector back to the terminals. Each terminal then computes the allocation vector for its connections. We want to study what aggregated information the terminals should send and what allocation problem should the controller and the terminals solve to produce a near-optimal (in terms of fairness) allocation vector. We propose a primal-based decomposition approach, examine in detail a number of approximations and show that by transmitting its total demand and number of connections, each terminal can achieve a near-optimal and near-fair allocation of capacity.