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Active queue management (AQM) mechanisms manage queue lengths by dropping packets when congestion is building up; end-systems can then react to such losses by reducing their packet rate, hence avoiding severe congestion. They are also very useful for the differentiated forwarding of packets in the DiffServ architecture. Many studies have shown that setting the parameters of an AQM algorithm may prove difficult and error-prone, and that the performance of AQM mechanisms is very sensitive to network conditions. The adaptive RIO mechanism (A-RIO) addresses both issues. It requires a single parameter, the desired queuing delay and adjusts its internal dynamics accordingly. A-RIO has been thoroughly evaluated in terms of delay response and network utilization but no study has been conducted in order to evaluate its behaviour in terms of fairness. By way of ns-2 simulations, This work examines A-RIO's ability to fairly share the network's resources (bandwidth) between the flows contending for those resources. Using Jain's fairness index as our performance metric, we compare the bandwidth distribution among flows obtained with A-RIO and with RIO.