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The problem of time-optimal network queue control is solved: what are the input data rates that make network queue sizes converge to their ideal size in the least possible time after a disturbance while still maintaining maximum link utilization at all times, even in the transient? The problem is nontrivial especially because of the vast possible heterogeneity in packet propagation delays in the network. In this paper, we derive the time-optimal queue control for a single congested network node with a single finite queue shared by flows with arbitrary network delays. We neatly separate the derivation of the optimal arrival rate sequence from that of the feedback control protocol to achieve it. The time-optimal control is robust to bandwidth and queue size estimation errors. Its complexity is only a function of the size of the network delays and no per-flow computation is needed. The time-optimality and robustness properties are proven to hold under all queue operating regimes with no need for linearizing approximations.