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 multi-fractal 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 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.