AgaBoogaBoo, I don't know what they're defining "deterministic networks", but SONET is a ring like TR and FDDI, and Extreme's EAPS and IEEE's in-progress ROR allow you to build rings out of Ethernet links.
Rings are a way to build self-healing networks that heal very quickly, because every node knows exactly what to do in case of a failure. With a shortest-path or spanning-tree topology network, you need topology change information to propogate everywhere before every node knows what to do about the failure, which inherently takes longer. In many environments, links/raw bandwidth is cheap, but reliability problems are very costly, so a "wasteful" network topology is fine.