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With the approval of IEEE P1901 standard for power line communications (PLC) and the recent Internet-enable home appliances like the IPTV having access to a content-on-demand service through the Internet as AcTVila in Japan, there is no doubt that PLC has taken a great step forward to emerge as the in-home-network technology. However, existing schemes developed so far have not considered the PLC network connected to an unstable Internet environment (i.e. more realistic situation). In this paper, we investigate the communication performance from the end-user perspective in such networks with large and variable round-trip time (RTT) and with the existence of cross-traffic. Then, we address the problem of unfair bandwidth allocation when multiple flows coexist and propose a TCP rate control considering the difference in terms of end-to-end delay and bandwidth to solve it. Our methodology was validated through simulations, and it effectively deals with the throughput unfairness problem under critical communication environment, where multiple flows with different RTTs share the PLC and cross-traffic exists on the path of the Internet.