3.2 KiB
| type | domain | description | confidence | source | created |
|---|---|---|---|---|---|
| claim | internet-finance | Time-varying arrival rates demand dynamic capacity scaling because constant sizing creates systematic mismatch | proven | Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016 | 2026-03-11 |
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
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.
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.
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.
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.
Evidence
- Whitt et al. (2016) prove that constant capacity sizing fails for non-stationary arrivals regardless of whether constant is set to average or maximum
- Time-varying arrival rates require capacity that tracks the rate function, not a single constant value
- The paper extends square-root staffing to handle both non-stationarity (time-varying rates) and non-Poisson characteristics (burstiness) simultaneously
Application to Pipeline Systems
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).
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.
Relevant Notes:
- domains/internet-finance/_map
Topics:
- core/mechanisms/_map