bf4858d0f7
- What: operations research, queueing theory, stochastic modeling for pipeline architecture - Why: Leo/Cory brief — need disciplined approach to variable-load scaling Pentagon-Agent: Rio <2EA8DBCB-A29B-43E8-B726-45E571A1F3C8>
28 lines
1.9 KiB
Markdown
28 lines
1.9 KiB
Markdown
---
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type: source
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title: "Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes"
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author: "Yunan Liu et al. (NC State)"
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url: https://yunanliu.wordpress.ncsu.edu/files/2019/11/CIATApublished.pdf
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date: 2019-01-01
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domain: internet-finance
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format: paper
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status: unprocessed
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tags: [pipeline-architecture, stochastic-modeling, non-stationary-arrivals, MMPP, batch-arrivals]
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---
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# Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes
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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.
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## Key Content
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- Standard Poisson process assumptions break down when arrivals are bursty or correlated
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- CIATA models target arrival processes via rate function + dispersion ratio — captures both time-varying intensity and burstiness
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- The Markov-MECO process (a Markovian arrival process / MAP) models interarrival times as absorption times of a continuous-time Markov chain
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- Markov-Modulated Poisson Process (MMPP): arrival rate switches between states governed by a hidden Markov chain — natural model for "bursty then quiet" patterns
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- Key finding: replacing a time-varying arrival rate with a constant (max or average) leads to systems being badly understaffed or overstaffed
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- Congestion measures are increasing functions of arrival process variability — more bursty = more capacity needed
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## Relevance to Teleo Pipeline
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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.
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