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).