569d4618c2
- What: square-root staffing law, Halfin-Whitt QED regime, variance pooling economies of scale - Why: Ward Whitt (Columbia) practitioner guide on queueing theory — foundational mechanism design results applicable to any multi-server pipeline - Connections: relates to foundations/critical-systems variance and resilience claims Pentagon-Agent: Rio <2EA8DBCB-A29B-43E8-B726-45E571A1F3C8>
36 lines
2.3 KiB
Markdown
36 lines
2.3 KiB
Markdown
---
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type: source
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title: "What You Should Know About Queueing Models"
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author: "Ward Whitt (Columbia University)"
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url: https://www.columbia.edu/~ww2040/shorter041907.pdf
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date: 2019-04-19
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domain: internet-finance
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format: paper
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status: processed
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processed_by: rio
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processed_date: 2026-03-12
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claims_extracted:
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- "square-root staffing sets optimal server count at base load plus beta times its square root making excess capacity scale sublinearly with demand"
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- "the Halfin-Whitt QED regime simultaneously achieves near-full server utilization and bounded delay because utilization approaches one at rate proportional to one over root n"
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- "pooling demand across servers reduces required excess capacity because total variance grows as the square root of n while demand grows as n"
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enrichments: []
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tags: [pipeline-architecture, operations-research, queueing-theory, square-root-staffing, Halfin-Whitt]
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---
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# What You Should Know About Queueing Models
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Practitioner-oriented guide by Ward Whitt (Columbia), one of the founders of modern queueing theory for service systems. Covers the essential queueing models practitioners need and introduces the Halfin-Whitt heavy-traffic regime.
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## Key Content
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- Square-root staffing principle: optimal server count = base load + β√(base load), where β is a quality-of-service parameter
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- The Halfin-Whitt (QED) regime: systems operate near full utilization while keeping delays manageable — utilization approaches 1 at rate Θ(1/√n) as servers n grow
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- Economies of scale in multi-server systems: larger systems need proportionally fewer excess servers
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- Practical formulas for determining server counts given arrival rates and service level targets
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- Erlang C formula as the workhorse for staffing calculations
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## Relevance to Teleo Pipeline
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The square-root staffing rule is directly applicable: if our base load requires R workers at full utilization, we should provision R + β√R workers where β ≈ 1-2 depending on target service level. For our scale (~8 sources/cycle, ~5 min service time), this gives concrete worker count guidance.
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Critical insight: you don't need to match peak load with workers. The square-root safety margin handles variance efficiently. Over-provisioning for peak is wasteful; under-provisioning for average causes queue explosion. The sweet spot is the QED regime.
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