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- 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>
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1.9 KiB
| type | title | author | url | date | domain | format | status | tags | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| source | Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes | Yunan Liu et al. (NC State) | https://yunanliu.wordpress.ncsu.edu/files/2019/11/CIATApublished.pdf | 2019-01-01 | internet-finance | paper | unprocessed |
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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.