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Network flow control mechanisms that are aware of global conditions potentially can achieve higher performance than flow control mechanisms that are only locally aware. Owing to high implementation overhead, globally-aware flow control mechanisms in their purest form are seldom adopted in practice, leading to less efficient simplified implementations. In this paper, we propose an efficient implementation of a globally-aware flow control mechanism, called Critical Bubble Scheme, and apply it successfully to k-ary n-cube networks for the general class of buffer occupancy-based network flow control techniques. Simulation results show that the proposed scheme can reduce the buffer access portion of packet latency by as much as 77%, leading to much lower average packet latency at medium and high network loads while sustaining 11% throughput improvement after network saturation.