47 lines
No EOL
2.6 KiB
Markdown
47 lines
No EOL
2.6 KiB
Markdown
---
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type: claim
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domain: internet-finance
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description: "Standard queueing formula that practitioners use to determine server counts from operational parameters"
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confidence: proven
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source: "Ward Whitt, What You Should Know About Queueing Models (2019)"
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created: 2026-03-11
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---
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# Erlang C formula is the computational workhorse for multi-server queue staffing calculations given arrival rates and service level targets
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The Erlang C formula (also called the Erlang delay formula) is the standard tool practitioners use to determine how many servers are needed to meet service level targets given arrival rates and service times. It calculates the probability that an arriving customer must wait (rather than immediately finding an available server) in an M/M/n queue.
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Whitt identifies this as "the workhorse for staffing calculations" in service operations. Given:
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- λ = arrival rate (customers per unit time)
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- μ = service rate per server (customers per unit time per server)
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- n = number of servers
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- Target service level (e.g., "80% of customers wait less than 20 seconds")
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The Erlang C formula determines whether n servers will meet the target, allowing practitioners to solve for the minimum n that satisfies their service level agreement.
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## Relationship to Square-Root Staffing
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The square-root staffing rule (n = R + β√R) is the asymptotic approximation that emerges from Erlang C analysis in the heavy-traffic regime. For large systems, the square-root rule gives the answer directly without needing to compute Erlang C iteratively.
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For small systems or when exact calculations are needed, practitioners use Erlang C directly. For large systems or quick estimates, the square-root rule suffices.
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## Practical Application
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For pipeline systems:
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1. Measure arrival rate λ (sources per hour)
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2. Measure service time 1/μ (minutes per source)
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3. Define service level target (e.g., "95% of sources processed within 1 hour")
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4. Use Erlang C to determine minimum worker count
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5. Validate that result approximates R + β√R for some β ≈ 1-2
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The Erlang C calculation accounts for the specific service level target, while the square-root rule gives the general scaling relationship.
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---
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Relevant Notes:
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- [[square-root-staffing-rule-provisions-servers-as-base-load-plus-beta-times-square-root-of-base-load-where-beta-controls-service-quality]] <!-- claim pending -->
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- [[halfin-whitt-qed-regime-enables-high-utilization-with-bounded-delays-by-approaching-full-load-at-rate-proportional-to-inverse-square-root-of-server-count]] <!-- claim pending -->
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Topics:
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- core/mechanisms/_map
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- domains/internet-finance/_map |