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Multipath transport protocols, which transmit data over multiple distinct paths in an end-to-end connection are introduced. However, they have a problem in terms of fairness. When the transmissions along several paths share the same bottleneck link, the multipath connection receives higher throughput than a competing regular TCP flow, because it executes congestion control per path with the same algorithm as TCP. We investigate a congestion control scheme that addresses this problem with the weighted congestion control approach. In our scheme, an end-to-end connection that uses flows along multiple paths can fairly compete with TCP flows at the shared bottleneck. Our scheme also maximizes the utilization of different path characteristics, such as bandwidth capacity and RTT. Our simulation results show that a bundle of multiple flows based on our scheme fairly competes with TCP flows at the shared bottleneck.