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TCP traffic has been reported to have not only self-similarity but also a multi-fractal nature. The multi-fractal nature of traffic volume in general is well known to have a significant influence on queueing behavior in short time scales. In our previous study, we showed that the retransmission time out (RTO) mechanism plays an important role in the multi-fractal nature of TCP traffic. In this paper, we investigate how to control the multifractal nature of TCP traffic in a real network. Here we focus on the random early detection (RED) mechanism in order to reduce the occurrence of RTO. We evaluate the RED mechanism from the viewpoint of its multi-fractal nature and show that the RED mechanism improves not only throughput and delay performance, but also the multi-fractal nature of TCP traffic.