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40 lines
3.2 KiB
Markdown
40 lines
3.2 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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tags: [pipeline-architecture, operations-research, queueing-theory, square-root-staffing, Halfin-Whitt]
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processed_by: rio
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processed_date: 2026-03-11
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claims_extracted: ["square-root-staffing-principle-provisions-servers-as-base-load-plus-beta-times-square-root-of-base-load-where-beta-is-quality-of-service-parameter.md", "halfin-whitt-qed-regime-enables-systems-to-operate-near-full-utilization-while-maintaining-service-quality-through-utilization-approaching-one-at-rate-one-over-square-root-n.md", "multi-server-queueing-systems-exhibit-economies-of-scale-because-safety-margin-grows-sublinearly-with-system-size.md"]
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extraction_model: "anthropic/claude-sonnet-4.5"
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extraction_notes: "Extracted three proven claims about queueing theory fundamentals: square-root staffing principle, Halfin-Whitt QED regime, and economies of scale in multi-server systems. All claims are foundational results from operations research with direct applicability to pipeline architecture and resource provisioning. Source is practitioner-oriented guide by Ward Whitt, a founder of modern queueing theory. No entities to extract (theoretical paper, no companies/products/decisions). No enrichments (queueing theory is new domain for KB)."
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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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## Key Facts
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- Erlang C formula is the computational workhorse for staffing calculations in multi-server queues
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- Square-root staffing formula: optimal servers = R + β√R where R is base load and β ≈ 1-2 for typical service levels
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- Halfin-Whitt regime characterized by utilization approaching 1 at rate Θ(1/√n) as servers n grow
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