I think II can be thought of as like the slowest link in the pipeline, which is why it plays an important role in this equation. Whereas L is the time we need to add for the first iteration, for the pipeline to "get warmed up."

Really, I think this equation is not controller/Spatial specific--I see it as applying to pipelined systems in general.

If the implicit pipeline in the inner controller introduces dependencies, will Spatial handle them on its own or raise a concern with the programmer?

The graph at the bottom right helps to explain the formula for T too. Here iters = n + 1 and L is the length for each iteration. So the total number of cycles T can thought of as adding up n initiation intervals and the last iteration n.

Do we know in advance how many iterations there are? If we don't know, then it might not be a pipeline-efficient program

Never mind, just realized that we do know the # of iterations... @I-henken Great question. I don't know it for sure, but I think in general pipelines will have control units to detect dependencies, and stall the pipeline to wait for dependencies to be resolved.