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Router-assisted congestion control protocols, also known as explicit rate notification (ERN) protocols, implement complex algorithms inside a router in order to provide both high link utilization and high fairness. Thus, router-assisted approaches overcome most of the end-to-end protocols problems in large bandwidth-delay product networks. Today, router-assisted protocols cannot be deployed in heterogeneous networks (e.g., Internet) due to their non-compliance with current network protocols. Nevertheless, these approaches can be deployed in satellite networks in the context of splitting PEPs. In this work, as router-assisted protocols can use TCP algorithms to enable reliability, we aim at understanding and providing a detailed view of the impact of such algorithms on the performance obtained by router-assisted protocols over satellite links. In particular, we both study XCP and P-XCP proposals over long delay, lossy and asymmetric links and propose an ns-2 implementation of the P-XCP protocol to the satellite community. To the best of our knowledge, this study is the first one which tackles the impact of TCP internal mechanisms on XCP protocol. Our main conclusion is that P-XCP on TCP new Reno slow but steady variant is to date, the most optimal configuration for satellite proxies.