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

type	title	author	url	date	domain	format	status	tags	processed_by	processed_date	claims_extracted	extraction_model	extraction_notes
source	Staffing a Service System with Non-Poisson Non-Stationary Arrivals	Ward Whitt et al. (Cambridge Core)	https://www.cambridge.org/core/journals/probability-in-the-engineering-and-informational-sciences/article/abs/staffing-a-service-system-with-nonpoisson-nonstationary-arrivals/0F42FDA80A8B0B197D3D9E0B040A43D2	2016-01-01	internet-finance	paper	processed	pipeline-architecture operations-research stochastic-modeling non-stationary-arrivals capacity-sizing	rio	2026-03-11	square-root-staffing-formula-requires-peakedness-adjustment-for-non-poisson-arrivals.md time-varying-arrival-rates-require-dynamic-staffing-not-constant-max-workers.md	anthropic/claude-sonnet-4.5	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

Extends the square-root staffing formula to handle non-Poisson arrival processes, including non-stationary Cox processes where the arrival rate itself is a stochastic process.

Key Content

• Standard Poisson assumption fails when arrivals are bursty or time-varying
• Introduces "peakedness" — the variance-to-mean ratio of the arrival process — as the key parameter for non-Poisson adjustment
• Modified staffing formula: adjust the square-root safety margin by the peakedness factor
• For bursty arrivals (peakedness > 1), you need MORE safety capacity than Poisson models suggest
• For smooth arrivals (peakedness < 1), you need LESS
• Practical: replacing time-varying arrival rates with constant (average or max) leads to badly under- or over-staffed systems

Relevance to Teleo Pipeline

Our arrival process is highly non-stationary: research dumps are bursty (15 sources at once), futardio launches come in bursts of 20+, while some days are quiet. This is textbook non-Poisson non-stationary. The peakedness parameter captures exactly how bursty our arrivals are and tells us how much extra capacity we need beyond the basic square-root staffing rule.

Key insight: using a constant MAX_WORKERS regardless of current queue state is the worst of both worlds — too many workers during quiet periods (wasted compute), too few during bursts (queue explosion).