A routing mechanism includes two acyclic non-adaptive virtual channels having two types of virtual channel buffers to store packets along deterministic virtual paths between nodes in an n-dimensional networked system, and an adaptive virtual channel having a third type of virtual channel buffer to store the packets along non-deterministic virtual paths between the nodes. The packets are routed between the nodes along either selected portions of the deterministic virtual paths or selected portions of the non-deterministic virtual paths based on routing information such that a packet is never routed on a selected portion of one of the non-deterministic virtual paths unless the third type virtual channel buffer associated with the selected portion of the one non-deterministic virtual path has sufficient space available to store the entire packet.