In one embodiment, a computer network may include nodes and at least one root node. A first subset of the nodes may be located along a designated path (a directed acyclic graph (DAG)) through the computer network to the root node, where the first subset of nodes is configured to operate according to a first wake-up timer. A second subset of the nodes that are not along the designated path are in communication to at least one node of the first subset of nodes along the designated path, and operate according to a second wake-up timer that is longer than the first wake-up timer. In this manner, second subset of nodes may be awake less often, e.g., conserving energy.