IV · Queueing theory
Universal scalability law
What it is
C(N) = N / (1 + α(N−1) + βN(N−1)). Throughput as a function of concurrency, with contention α and coherence-cost β.
Where it lives
Choosing thread counts, replica counts, partition counts. Where adding more workers makes things worse.
The key insight
Above a critical N, throughput peaks and then drops. β captures coordination costs that grow as O(N²).