The Multi-Path Transmission Control Protocol (MPTCP) is the new concurrent multi-path transfer extension for the widely-deployed Transmission Control Protocol (TCP). Of course, having multiple and possibly highly dissimilar paths for transmission is a challenge for the management of the send and receive buffers, since optimal throughput is desired with a reasonable allocation of the limited memory resources in MPTCP endpoints. This is particularly important when many MPTCP connections have to be handled simultaneously. This paper measures out the required MPTCP buffer size in the real-world Internet testbed NorNet, comparing theoretical size and real size to analyse MPTCP performance. The experiment shows that multi-path transmission can effectively increase the application payload throughput, and greatly improve the robustness of the data transmission. As an important point of this paper, we can show that appropriate buffer size settings can increase the payload throughput, while not wasting resources. This paper has certain significance for further accurately determining the optimal buffer size settings for multi-path transmission in large-scale Internet setups.