Modules D01, D05 · concept player

Amdahl bends, then communication turns it over

Amdahl's law says a fixed problem's speedup flattens toward 1/s and never crosses it. Add a communication term and the curve does something Amdahl alone never predicts: past some rank count, it turns over and going wider makes you slower.

Exact calculus on the stated model, not a measured cluster. Total time is normalized to s + (1−s)/p + αp; the turnover point p* = √((1−s)/α) falls straight out of setting its derivative to zero. No multi-node measurement exists anywhere in this repository — every inter-node figure here is an analytic model and says so, the same disclosure D01's lab carries in its own output banner. D01 section 3 derives the full alpha-beta form; this page uses the simplified per-rank term that produces the same qualitative turnover.