bf4858d0f7
- What: operations research, queueing theory, stochastic modeling for pipeline architecture - Why: Leo/Cory brief — need disciplined approach to variable-load scaling Pentagon-Agent: Rio <2EA8DBCB-A29B-43E8-B726-45E571A1F3C8>
29 lines
1.6 KiB
Markdown
29 lines
1.6 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: unprocessed
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tags: [pipeline-architecture, operations-research, queueing-theory, littles-law, capacity-planning]
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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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