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, for k-ary n-cube networks. This scheme achieves near-optimal performance with the same minimal buffer requirements of globally-aware flow control and can be further generalized to implement the general class of buffer occupancy-based network flow control. We prove deadlock freedom of the proposed scheme and exploit its use in handling protocol-induced deadlocks in on-chip environments. We evaluate the proposed scheme using both synthetic traffic and real application loads. Simulation results show that the proposed scheme can reduce the buffer access component of packet latency by as much as 62% over locally-aware flow control, and improve average packet latency by 18.8% and overall execution time by 7.2% in full system simulation.