extract: 2016-00-00-cambridge-staffing-non-poisson-non-stationary-arrivals

Pentagon-Agent: Ganymede <F99EBFA6-547B-4096-BEEA-1D59C3E4028A>

domains/internet-finance/square-root-staffing-formula-requires-peakedness-adjustment-for-non-poisson-arrivals.md

@@ -0,0 +1,36 @@
+---
+type: claim
+domain: internet-finance
+description: "Bursty arrival processes require more safety capacity than Poisson models predict, scaled by variance-to-mean ratio"
+confidence: proven
+source: "Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016"
+created: 2026-03-11
+---
+
+# Square-root staffing formula requires peakedness adjustment for non-Poisson arrivals because bursty processes need proportionally more safety capacity than the Poisson baseline predicts
+
+The standard square-root staffing formula (workers = mean load + safety factor × √mean) assumes Poisson arrivals where variance equals mean. Real-world arrival processes violate this assumption through burstiness (arrivals clustered in time) or smoothness (arrivals more evenly distributed than random).
+
+Whitt et al. extend the square-root staffing rule by introducing **peakedness** — the variance-to-mean ratio of the arrival process — as the key adjustment parameter. For bursty arrivals (peakedness > 1), systems require MORE safety capacity than Poisson models suggest. For smooth arrivals (peakedness < 1), systems need LESS.
+
+The modified staffing formula adjusts the square-root safety margin by multiplying by the square root of peakedness. This correction is critical for non-stationary systems where arrival rates vary over time (daily cycles, seasonal patterns, or event-driven spikes).
+
+## Evidence
+
+- Whitt et al. (2016) prove that peakedness — the variance-to-mean ratio — captures the essential non-Poisson behavior for staffing calculations
+- Standard Poisson assumption (variance = mean) fails empirically for bursty workloads like research paper dumps, product launches, or customer service spikes
+- Using constant staffing (fixed MAX_WORKERS) regardless of queue state creates dual failure: over-provisioning during quiet periods (wasted compute) and under-provisioning during bursts (queue explosion)
+
+## Relevance to Pipeline Architecture
+
+Teleo's research pipeline exhibits textbook non-Poisson non-stationary arrivals: research dumps arrive in bursts of 15+ sources, futardio launches come in waves of 20+ proposals, while other days see minimal activity. The peakedness parameter quantifies exactly how much extra capacity is needed beyond naive square-root staffing.
+
+This directly informs dynamic worker scaling: measure empirical peakedness from historical arrival data, adjust safety capacity accordingly, and scale workers based on current queue depth rather than using fixed limits.
+
+---
+
+Relevant Notes:
+- domains/internet-finance/_map
+
+Topics:
+- core/mechanisms/_map

domains/internet-finance/time-varying-arrival-rates-require-dynamic-staffing-not-constant-max-workers.md

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+---
+type: claim
+domain: internet-finance
+description: "Replacing non-stationary arrival rates with constant staffing leads to systematic over- or under-provisioning"
+confidence: proven
+source: "Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016"
+created: 2026-03-11
+---
+
+# Time-varying arrival rates require dynamic staffing not constant MAX_WORKERS because using average or maximum rates as constants creates systematic misallocation across the arrival cycle
+
+Non-stationary arrival processes — where the arrival rate itself changes over time — cannot be efficiently staffed with constant worker counts. Whitt et al. demonstrate that replacing time-varying rates with either the average rate or the maximum rate produces badly mis-staffed systems:
+
+- **Constant = average rate**: Under-staffed during peak periods, leading to queue explosions and service degradation
+- **Constant = maximum rate**: Over-staffed during off-peak periods, wasting capacity and compute resources
+
+The optimal approach tracks the arrival rate over time and adjusts staffing dynamically to match the current load plus an appropriate safety margin (scaled by peakedness for non-Poisson processes).
+
+## Evidence
+
+- Whitt et al. (2016) prove that time-varying arrival rates require time-varying staffing levels for efficiency
+- Constant staffing at maximum capacity wastes resources during low-traffic periods
+- Constant staffing at average capacity fails catastrophically during burst periods
+- Dynamic staffing based on current queue state and arrival rate estimates achieves both efficiency (no waste during quiet periods) and reliability (adequate capacity during bursts)
+
+## Application to Teleo Pipeline
+
+Teleo's research processing pipeline exhibits strong non-stationarity: research dumps and futardio launches create burst periods with 15-20+ simultaneous arrivals, while other periods see minimal activity. Using a fixed MAX_WORKERS setting (constant staffing) is the worst of both worlds:
+
+- During bursts: MAX_WORKERS is too low, queue explodes, processing stalls
+- During quiet periods: MAX_WORKERS is too high, workers sit idle, compute wasted
+
+Dynamic worker scaling based on current queue depth and estimated arrival rate (with peakedness adjustment) is the theoretically correct solution.
+
+---
+
+Relevant Notes:
+- [[square-root-staffing-formula-requires-peakedness-adjustment-for-non-poisson-arrivals]]
+- domains/internet-finance/_map
+
+Topics:
+- core/mechanisms/_map

inbox/archive/2016-00-00-cambridge-staffing-non-poisson-non-stationary-arrivals.md

@@ -6,8 +6,13 @@ url: https://www.cambridge.org/core/journals/probability-in-the-engineering-and-
 date: 2016-01-01
 domain: internet-finance
 format: paper
-status: unprocessed
+status: processed
 tags: [pipeline-architecture, operations-research, stochastic-modeling, non-stationary-arrivals, capacity-sizing]
+processed_by: rio
+processed_date: 2026-03-11
+claims_extracted: ["square-root-staffing-formula-requires-peakedness-adjustment-for-non-poisson-arrivals.md", "time-varying-arrival-rates-require-dynamic-staffing-not-constant-max-workers.md"]
+extraction_model: "anthropic/claude-sonnet-4.5"
+extraction_notes: "Operations research paper on staffing under non-Poisson non-stationary arrivals. Extracted two claims on peakedness adjustment and dynamic staffing requirements. Direct application to Teleo pipeline architecture for worker scaling. No entity data (academic paper, no companies/products/decisions). No enrichments (novel theoretical contribution not covered by existing claims)."
 ---
 
 # Staffing a Service System with Non-Poisson Non-Stationary Arrivals