---
type: claim
domain: internet-finance
description: "CIATA method models time-varying bursty arrivals through combined rate and variance parameters"
confidence: proven
source: "Liu et al. (NC State), 'Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes' (2019)"
created: 2026-03-11
sourced_from:
- inbox/archive/internet-finance/2019-00-00-liu-modeling-nonstationary-non-poisson-arrival-processes.md
---

# 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.

---

Relevant Notes:
- domains/internet-finance/_map

Topics:
- core/mechanisms/_map