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We present a competition detection mechanism for parallel TCP flows and use this to propose a new parallel TCP congestion control scheme called adaptive TCP-P (A-TCP-P). A-TCP-P automatically controls the aggregated aggressiveness of parallel TCP flows to fairly share network bandwidth with single TCP flows independently from the number of the parallel TCP flows while effectively utilizing available bandwidth when it does not detect competition. A-TCP-P realizes this by adaptively adjusting the aggregated aggressiveness of parallel TCP flows according to network situations in a self-managed way. We implement A-TCP-P as a part of Linux kernel and the experimental results show that the proposed parallel TCP scheme improves per-host fairness and effectively utilize available bandwidth with reduced packet loss when it does not detect competing TCP flows from other hosts.