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Energy saving technologies are currently of significant concern in the Internet with the ever increasing traffic demand. Many studies have been conducted, but in general, they share one basic idea: dynamically controlling the transmission capacity to save power in response to the amount of arriving traffic. Thus, a flow will be transferred with a power-aware switch equipped with a dynamic transmission control scheme in the future Internet. We investigate how this dynamic transmission control affects the performance of the transmission control protocol. Based on this investigation, we propose a slow start scheme called measurement-based slow start (MSS) that takes into account congestion by calculating the round trip time. From simulation results, MSS can provide compound TCP (CTCP) with an effective slow start mechanism in the networks equipped with the dynamic link control scheme.