37 lines
3.2 KiB
Markdown
37 lines
3.2 KiB
Markdown
---
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type: claim
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domain: internet-finance
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description: "Time-varying arrival rates demand dynamic capacity scaling because constant sizing creates systematic mismatch"
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confidence: proven
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source: "Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016"
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created: 2026-03-11
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---
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# Non-stationary arrival processes require time-varying capacity not constant max sizing because static capacity creates systematic over-provisioning during quiet periods and under-provisioning during bursts
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When arrival rates vary over time (non-stationary processes), using constant capacity — whether sized for average load or peak load — creates systematic inefficiency. Average-based sizing causes queue explosions during high-arrival periods. Peak-based sizing wastes resources during low-arrival periods. Only time-varying capacity that tracks arrival rate patterns achieves efficient resource utilization.
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Whitt et al. demonstrate that non-stationary arrival processes (where the arrival rate itself changes over time) require fundamentally different staffing strategies than stationary processes. The paper shows that replacing time-varying arrival rates with constant rates — regardless of whether you use the average or maximum rate — produces badly mis-sized systems.
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This is not a theoretical edge case. Most real-world service systems face non-stationary arrivals: call centers have daily and weekly patterns, emergency rooms have time-of-day surges, content moderation systems face event-driven spikes. The standard approach of sizing for peak load wastes capacity during normal periods. Sizing for average load causes service degradation during predictable peaks.
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The key insight is that non-stationarity (time-varying rates) and non-Poisson characteristics (burstiness) are independent properties that both require adjustment. A system can have smooth but time-varying arrivals (non-stationary, peakedness = 1) or bursty but constant-rate arrivals (stationary, peakedness > 1). Real systems often exhibit both.
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## Evidence
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- Whitt et al. (2016) prove that constant capacity sizing fails for non-stationary arrivals regardless of whether constant is set to average or maximum
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- Time-varying arrival rates require capacity that tracks the rate function, not a single constant value
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- The paper extends square-root staffing to handle both non-stationarity (time-varying rates) and non-Poisson characteristics (burstiness) simultaneously
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## Application to Pipeline Systems
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Living Capital pipeline exhibits strong non-stationarity: research dumps cluster around funding cycles, futardio launches follow market sentiment waves, curator activity has weekly patterns. Using MAX_WORKERS as a constant ceiling wastes compute during quiet periods (most of the time) while still being insufficient during burst periods (when it matters most).
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The solution is time-varying capacity: measure historical arrival patterns, identify predictable time-of-day and day-of-week patterns, and scale worker pool dynamically. This requires tracking arrival timestamps and computing time-windowed arrival rates, not just queue depth.
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---
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Relevant Notes:
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- domains/internet-finance/_map
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Topics:
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- core/mechanisms/_map
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