Little's Law
L = λW. Items in system = arrival rate × average wait.
Origin
John D. C. Little proved it for general queueing systems in 1961 ("A Proof for the Queuing Formula: L = λW", Operations Research). Stunningly general — holds for any stable queue regardless of arrival or service distribution. Little's career was at MIT Sloan; he's still publishing.
Where it shows up in production
- Capacity planning Concurrent users = arrival rate × session time. 1k req/s × 100ms latency = 100 concurrent requests in flight.
- Connection pool sizing pool_size ≥ peak_qps × avg_query_duration. Postgres pool that's too small bottlenecks the whole system.
- Buffer sizing in Kafka producer batches: batch_size = throughput × linger_ms.
On Semicolony
Sources & further reading
Found this useful?