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TCP connection throughput is inversely proportional to the connection round trip time (RTT). To mitigate TCP bias to short RTT connections, a differentiated services traffic conditioner can ensure connections with long RTTs do not starve when connections with short RTTs get all extra resources after achieving the target rates. Current proposals for RTT-aware conditioners work well for a small number of connections when most TCP connections are in the congestion avoidance phase. If there is a large number of TCP connections, however, connections time-out and go to slow start. We show that current RTT-aware conditioners over-protect long RTT flows and starve short RTT flows in this case. We design and evaluate a conditioner based on RTT as well as the retransmission time-out (RTO). The proposed RTT-RTO aware traffic conditioner works well for realistic situations with a large number of connections. Simulation results in a variety of situations confirm that the conditioner mitigates RTT bias.