---
type: claim
domain: internet-finance
description: "Little's Law calculates theoretical minimum capacity but real systems need safety margin above that floor"
confidence: proven
source: "Dan Slimmon, 'Using Little's Law to Scale Applications' (2022-06-07)"
created: 2026-03-11
sourced_from:
- inbox/archive/internet-finance/2022-06-07-slimmon-littles-law-scale-applications.md
---

# Little's Law provides minimum worker capacity floor for pipeline systems but requires buffer margin for variance

Little's Law (L = λW) gives the theoretical minimum capacity for steady-state systems: total workers needed ≥ (arrival rate) × (average processing time). This is the floor, not the ceiling. Real systems require buffer capacity above this minimum to handle variance in arrival rates and processing times.

For a system processing 1000 requests/second with 0.34s average processing time, Little's Law calculates 340 concurrent requests needed at steady state. However, this assumes perfect uniformity. Production systems experience bursts, outliers, and cascading delays that the long-term average doesn't capture.

The formula is valuable for capacity planning because it establishes the lower bound — you cannot run below this threshold without queue buildup. But it's not a complete scaling solution. The gap between theoretical minimum and operational capacity is where queueing theory, square-root staffing rules, and empirical load testing fill in.

## Evidence

- 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 from source: 1000 req/s × 0.34s = 340 concurrent requests needed
- Source explicitly notes: "Little's Law gives long-term averages only — real systems need buffer capacity beyond the theoretical minimum to handle variance"

## Application to Pipeline Architecture

For Teleo pipeline: if processing ~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 workers must pipeline or queue buildup occurs.

More generally: λ = average sources per second, W = average extraction time. Total workers needed ≥ λ × W gives the minimum worker floor. Additional capacity rules (like square-root staffing) provide the safety margin above that floor.


### Additional Evidence (extend)
*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*

M/M/c queueing theory provides closed-form solutions for expected wait times given worker counts, enabling precise capacity planning beyond Little's Law's minimum floor. The framework connects arrival rate modeling to worker count optimization through explicit formulas that account for variance.

---

Relevant Notes:
- domains/internet-finance/_map

Topics:
- core/mechanisms/_map