In one embodiment, a root of a directed acyclic graph (DAG) may determine transmission of critical traffic from a first device to a second device in a computer network using the DAG, and may also determine a maximum tolerable delay of the critical traffic. As such, the root may compute, based on a known topology of the computer network, a constrained shortest path first (CSPF) point-to-point (P2P) path from the first device to the second device to meet the maximum tolerable delay. The root may then inform the first device of the P2P path to the second device to cause the first device to use the P2P path for the critical traffic.
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