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A novel congestion control protocol, ARROW-TCP, is proposed to address the issues of stability and convergence in existing transmission control protocols. Theoretical analysis shows that ARROW-TCP is globally stable and achieves exponential convergence to efficiency and fairness in a constant time. Meanwhile, ARROW-TCP obtains ideal performance of zero queuing delay, free packet loss by converging monotonically to the fair allocation and avoiding overshooting link capacity. Moreover, the price mechanism leverages ARROW-TCP into max-min rate allocation in hybrid multi-bottleneck networks. Finally, extensive simulations are conducted to verify our theoretical analysis and the simulation results demonstrate that ARROWTCP outperforms other transmission control protocols in terms of stability, convergence, and packet loss rate.