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2.2 KiB
Markdown
36 lines
No EOL
2.2 KiB
Markdown
---
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type: claim
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domain: internet-finance
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description: "Hidden Markov chain governs rate switching between active and quiet states"
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confidence: proven
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source: "Liu et al. (NC State), 'Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes' (2019)"
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created: 2026-03-11
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---
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# MMPP models session-based bursty arrivals through hidden state Markov chain
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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.
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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).
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## Evidence
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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.
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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.
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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.
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## Application to Capital Formation Pipelines
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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.
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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.
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---
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Relevant Notes:
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- domains/internet-finance/_map
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Topics:
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- core/mechanisms/_map |