---
type: claim
domain: internet-finance
description: "Hidden Markov chain governs rate switching between active and quiet states"
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
---

# MMPP models session-based bursty arrivals through hidden state Markov chain

Markov-Modulated Poisson Process (MMPP) provides a natural framework for modeling arrival processes that alternate between active and quiet periods. The arrival rate switches between discrete states governed by a continuous-time Markov chain, where the state transitions are hidden but the arrival rate in each state is observable.

This architecture directly captures "research session" dynamics where an unobservable state (researcher actively working vs. not working) determines whether arrivals occur at high rate (burst) or low rate (quiet).

## Evidence

Liu et al. define MMPP as a process where "arrival rate switches between states governed by a hidden Markov chain — natural model for 'bursty then quiet' patterns." The underlying Markov chain controls state transitions, while each state has an associated Poisson arrival rate.

The paper notes that "congestion measures are increasing functions of arrival process variability — more bursty = more capacity needed," establishing that MMPP's ability to model burstiness has direct operational implications for capacity planning.

The Markov-MECO process, a related Markovian arrival process (MAP), models "interarrival times as absorption times of a continuous-time Markov chain," providing the theoretical foundation for state-dependent arrival modeling.

## Application to Capital Formation Pipelines

Research-driven capital formation exhibits textbook MMPP behavior: during active research sessions, sources arrive in bursts of 10-20; during inactive periods, arrivals drop to 0-2 per day. The hidden state is whether a research session is active, and this state governs the arrival rate.

Capacity sizing for such processes requires modeling the state transition dynamics (session start/end rates) and the arrival rates in each state, not just the time-averaged arrival rate.

---

Relevant Notes:
- domains/internet-finance/_map

Topics:
- core/mechanisms/_map