40 lines
2.6 KiB
Markdown
40 lines
2.6 KiB
Markdown
---
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type: source
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title: "Using Little's Law to Scale Applications"
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author: "Dan Slimmon"
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url: https://blog.danslimmon.com/2022/06/07/using-littles-law-to-scale-applications/
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date: 2022-06-07
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domain: internet-finance
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format: essay
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status: processed
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tags: [pipeline-architecture, operations-research, queueing-theory, littles-law, capacity-planning]
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processed_by: rio
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processed_date: 2026-03-11
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claims_extracted: ["littles-law-provides-minimum-worker-capacity-floor-for-pipeline-systems-but-requires-buffer-margin-for-variance.md"]
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extraction_model: "anthropic/claude-sonnet-4.5"
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extraction_notes: "Single practitioner essay on queueing theory application. Extracted one claim about the gap between theoretical minimum and practical capacity requirements. The source provides clear operational guidance but is limited to one author's experience, justifying 'proven' confidence for the mathematical relationship while noting the practical caveat about variance. No entities to extract — this is pure mechanism discussion without organizational actors."
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---
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# Using Little's Law to Scale Applications
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Practitioner guide showing how Little's Law (L = λW) provides a simple but powerful tool for capacity planning in real systems.
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## Key Content
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- Little's Law: L = λW where L = average items in system, λ = arrival rate, W = average time per item
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- Rearranged for capacity: (total worker threads) ≥ (arrival rate)(average processing time)
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- Practical example: 1000 req/s × 0.34s = 340 concurrent requests needed
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- Important caveat: Little's Law gives long-term averages only — real systems need buffer capacity beyond the theoretical minimum to handle variance
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- The formula guides capacity planning but isn't a complete scaling solution — it's the floor, not the ceiling
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## Relevance to Teleo Pipeline
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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.
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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.
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## Key Facts
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- Little's Law formula: L = λW where L = average items in system, λ = arrival rate, W = average time per item
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- Rearranged for capacity planning: total worker threads ≥ (arrival rate)(average processing time)
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- Example calculation: 1000 req/s × 0.34s = 340 concurrent requests needed
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