In one embodiment, certain nodes in a computer network maintain a plurality of routing topologies, each associated with a different corresponding delay (e.g., dynamically adjusted). Upon receiving a packet with an indicated delay budget at a particular node, the node updates the delay budget based on an incurred delay up to and including the particular node since the indicated delay budget was last updated, and selects a particular routing topology on which to forward the packet based on the updated delay budget and the corresponding routing topology delays. The packet may then be forwarded with the updated delay budget on the selected routing topology, accordingly.