teleo-codex/inbox/archive/2022-06-07-slimmon-littles-law-scale-applications.md

type	title	author	url	date	domain	format	status	tags	processed_by	processed_date	claims_extracted	extraction_model	extraction_notes
source	Using Little's Law to Scale Applications	Dan Slimmon	https://blog.danslimmon.com/2022/06/07/using-littles-law-to-scale-applications/	2022-06-07	internet-finance	essay	processed	pipeline-architecture operations-research queueing-theory littles-law capacity-planning	rio	2026-03-11	littles-law-provides-minimum-worker-capacity-floor-for-pipeline-systems-but-requires-buffer-margin-for-variance.md	anthropic/claude-sonnet-4.5	Single practitioner guide on applying queueing theory to capacity planning. Extracted one claim about the gap between theoretical minimum and operational capacity requirements. The source is primarily instructional rather than making novel arguable propositions — most content is established operations research applied to web systems. Key insight is the explicit caveat that Little's Law provides floor not ceiling.

Using Little's Law to Scale Applications

Practitioner guide showing how Little's Law (L = λW) provides a simple but powerful tool for capacity planning in real systems.

Key Content

• Little's Law: L = λW where L = average items in system, λ = arrival rate, W = average time per item
• Rearranged for capacity: (total worker threads) ≥ (arrival rate)(average processing time)
• Practical example: 1000 req/s × 0.34s = 340 concurrent requests needed
• Important caveat: Little's Law gives long-term averages only — real systems need buffer capacity beyond the theoretical minimum to handle variance
• The formula guides capacity planning but isn't a complete scaling solution — it's the floor, not the ceiling

Relevance to Teleo Pipeline

Direct application: if we process ~8 sources per extraction cycle (every 5 min) and each takes ~10-15 min of Claude compute, Little's Law says L = (8/300s) × 750s ≈ 20 sources in-flight at steady state. With 6 workers, each handles ~3.3 sources concurrently — which means we need the workers to pipeline or we'll have queue buildup.

More practically: λ = average sources per second, W = average extraction time. Total workers needed ≥ λ × W. This gives us the minimum worker floor. The square-root staffing rule gives us the safety margin above that floor.

Key Facts

• Little's Law formula: L = λW (average items in system = arrival rate × average time per item)
• Capacity planning rearrangement: total workers ≥ (arrival rate)(average processing time)
• Example calculation: 1000 req/s × 0.34s = 340 concurrent requests minimum