Stochastic approximation based on-line algorithm for fairness in multi-rate wireless LANs

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It is well known that IEEE 802.11 based MAC provides max---min fairness to all nodes even in a multi-rate WLAN. However, the max---min fairness may not always be the preferred fairness criteria as it significantly reduces overall system throughput. In this paper, we explore the proportional fairness and the time fairness. First, we obtain a condition that must be satisfied by the attempt probabilities to achieve proportional fairness. Using this condition, we propose a stochastic approximation based on-line algorithm that tunes attempt probabilities to achieve proportional fairness. The proposed algorithm can be implemented in a distributed fashion, and can provide optimal performance even when node uses a rate adaptation scheme. Next, we show that the time fairness is a special case of weighted max---min fairness with the weight for a node is equal to its transmission rate. Thus, the existing algorithms to achieve weighted max---min fairness can be used to achieve time fairness as well. This exposition also demonstrates that the proportional fairness and the time fairness are not the same contrary to what was conjectured. Performance comparison of various fairness criteria is done through ns-3 simulations. Simulation results show that time fair schemes achieve the highest throughput, and the sum of logarithm of individual node's throughputs under the time fairness is close to that under a proportionally fair scheme.