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

type	domain	description	confidence	source	created
claim	internet-finance	Bursty arrival processes require more safety capacity than Poisson models predict, scaled by variance-to-mean ratio	proven	Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016	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.

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Relevant Notes:

• domains/internet-finance/_map

Topics:

• core/mechanisms/_map