teleo-codex/domains/internet-finance/nonstationary-non-poisson-arrival-modeling-requires-rate-function-plus-dispersion-ratio-to-capture-burstiness.md

type	domain	description	confidence	source	created
claim	internet-finance	CIATA method models time-varying bursty arrivals through combined rate and variance parameters	proven	Liu et al. (NC State), 'Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes' (2019)	2026-03-11

Nonstationary non-Poisson arrival modeling requires rate function plus dispersion ratio to capture burstiness

Standard Poisson process assumptions break down when arrivals exhibit correlation and burstiness. The CIATA (Combined Inversion-and-Thinning Approach) method models arrival processes through two parameters: a rate function λ(t) capturing time-varying intensity, and an asymptotic variance-to-mean (dispersion) ratio capturing burstiness beyond what the rate alone predicts.

This two-parameter approach is necessary because time-varying rate alone cannot capture the correlation structure of bursty arrivals. A process with constant high variance but varying rate behaves fundamentally differently from a Poisson process with the same rate function.

Evidence

Liu et al. demonstrate that CIATA models "target arrival processes via rate function + dispersion ratio — captures both time-varying intensity and burstiness." The paper shows that "replacing a time-varying arrival rate with a constant (max or average) leads to systems being badly understaffed or overstaffed," proving that rate variation alone is insufficient.

The Markov-Modulated Poisson Process (MMPP) framework provides the theoretical foundation: "arrival rate switches between states governed by a hidden Markov chain — natural model for 'bursty then quiet' patterns." This captures the correlation structure that pure rate functions miss.

Relevance to Internet Finance

This modeling framework directly applies to capital formation pipelines where research sessions create bursts of 10-20 source arrivals followed by quiet periods of 0-2 per day. The hidden state (research session active vs. inactive) governs the arrival rate, making this a textbook MMPP application.

Capacity planning based on average arrival rates will systematically fail for such processes, leading to either chronic congestion during bursts or wasteful overcapacity during quiet periods.

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