---
type: source
title: "Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes"
author: "Yunan Liu et al. (NC State)"
url: https://yunanliu.wordpress.ncsu.edu/files/2019/11/CIATApublished.pdf
date: 2019-01-01
domain: internet-finance
format: paper
status: processed
tags: [pipeline-architecture, stochastic-modeling, non-stationary-arrivals, MMPP, batch-arrivals]
processed_by: rio
processed_date: 2026-03-11
claims_extracted: ["nonstationary-non-poisson-arrival-modeling-requires-rate-function-plus-dispersion-ratio-to-capture-burstiness.md", "mmpp-models-session-based-bursty-arrivals-through-hidden-state-markov-chain.md", "constant-rate-approximation-of-time-varying-arrivals-causes-systematic-staffing-errors.md", "arrival-process-burstiness-increases-required-capacity-for-fixed-service-level.md"]
extraction_model: "anthropic/claude-sonnet-4.5"
extraction_notes: "Extracted four claims on nonstationary non-Poisson arrival modeling. Source provides theoretical foundation for MMPP modeling of bursty research pipeline arrivals. Key insight: rate function alone insufficient—dispersion ratio required to capture burstiness. Direct application to capital formation pipeline capacity planning where research sessions create burst arrivals. All claims rated 'proven' as this is peer-reviewed operations research establishing fundamental queueing theory results."
---

# Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes

Introduces the CIATA (Combined Inversion-and-Thinning Approach) method for modeling nonstationary non-Poisson processes characterized by a rate function, mean-value function, and asymptotic variance-to-mean (dispersion) ratio.

## Key Content

- Standard Poisson process assumptions break down when arrivals are bursty or correlated
- CIATA models target arrival processes via rate function + dispersion ratio — captures both time-varying intensity and burstiness
- The Markov-MECO process (a Markovian arrival process / MAP) models interarrival times as absorption times of a continuous-time Markov chain
- Markov-Modulated Poisson Process (MMPP): arrival rate switches between states governed by a hidden Markov chain — natural model for "bursty then quiet" patterns
- Key finding: replacing a time-varying arrival rate with a constant (max or average) leads to systems being badly understaffed or overstaffed
- Congestion measures are increasing functions of arrival process variability — more bursty = more capacity needed

## Relevance to Teleo Pipeline

Our arrival process is textbook MMPP: there's a hidden state (research session happening vs. quiet period) that governs the arrival rate. During research sessions, sources arrive in bursts of 10-20. During quiet periods, maybe 0-2 per day. The MMPP framework models this directly and gives us tools to size capacity for the mixture of states rather than the average.


## Key Facts
- CIATA = Combined Inversion-and-Thinning Approach for modeling nonstationary non-Poisson processes
- MMPP = Markov-Modulated Poisson Process where hidden Markov chain governs rate state transitions
- MAP = Markovian Arrival Process, generalization of MMPP
- Markov-MECO models interarrival times as absorption times of continuous-time Markov chain
