extract: 2025-04-25-bournassenko-queueing-theory-cicd-pipelines #990

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@ -33,6 +33,12 @@ The multiplicative decrease (halving workers on congestion) provides rapid respo
This is an application of proven AIMD theory to a specific system architecture, but the actual performance in the Teleo pipeline context is untested. The claim that AIMD is "perfect for" this setting is theoretical—empirical validation would strengthen confidence from experimental to likely. This is an application of proven AIMD theory to a specific system architecture, but the actual performance in the Teleo pipeline context is untested. The claim that AIMD is "perfect for" this setting is theoretical—empirical validation would strengthen confidence from experimental to likely.
### Additional Evidence (extend)
*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
M/M/c queueing theory provides the theoretical foundation for why AIMD-style reactive scaling works: the queue depth signal directly maps to utilization in multi-server systems, and the diminishing returns curve means aggressive scaling is only needed near saturation.
--- ---
Relevant Notes: Relevant Notes:

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@ -28,6 +28,12 @@ For Teleo pipeline: if processing ~8 sources per extraction cycle (every 5 min)
More generally: λ = average sources per second, W = average extraction time. Total workers needed ≥ λ × W gives the minimum worker floor. Additional capacity rules (like square-root staffing) provide the safety margin above that floor. More generally: λ = average sources per second, W = average extraction time. Total workers needed ≥ λ × W gives the minimum worker floor. Additional capacity rules (like square-root staffing) provide the safety margin above that floor.
### Additional Evidence (confirm)
*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
The paper explicitly uses Little's Law as the foundation for minimum capacity calculation in CI/CD pipelines, then extends it with M/M/c analysis to account for variance and determine optimal buffer margins.
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Relevant Notes: Relevant Notes:

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@ -26,6 +26,12 @@ From the SIAM Review tutorial:
For systems in the 5-6 worker range, sophisticated dynamic algorithms provide minimal benefit over simple threshold policies informed by queueing theory. The economies-of-scale result also indicates that marginal value per worker decreases as systems grow beyond 20+ workers, which is critical for cost optimization in scaled deployments. For systems in the 5-6 worker range, sophisticated dynamic algorithms provide minimal benefit over simple threshold policies informed by queueing theory. The economies-of-scale result also indicates that marginal value per worker decreases as systems grow beyond 20+ workers, which is critical for cost optimization in scaled deployments.
### Additional Evidence (extend)
*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
Bournassenko's CI/CD pipeline application demonstrates that square-root staffing principles from call center theory generalize to software build systems, validating the principle across domains with different arrival patterns and service time distributions.
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Relevant Notes: Relevant Notes:

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@ -0,0 +1,26 @@
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"missing_attribution_extractor"
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@ -6,8 +6,12 @@ url: https://arxiv.org/abs/2504.18705
date: 2025-04-25 date: 2025-04-25
domain: internet-finance domain: internet-finance
format: paper format: paper
status: unprocessed status: enrichment
tags: [pipeline-architecture, operations-research, queueing-theory, ci-cd, M/M/c-queue] tags: [pipeline-architecture, operations-research, queueing-theory, ci-cd, M/M/c-queue]
processed_by: rio
processed_date: 2026-03-16
enrichments_applied: ["square-root-staffing-principle-achieves-economies-of-scale-in-queueing-systems-by-operating-near-full-utilization-with-manageable-delays.md", "aimd-scaling-solves-variable-load-expensive-compute-coordination-without-prediction.md", "littles-law-provides-minimum-worker-capacity-floor-for-pipeline-systems-but-requires-buffer-margin-for-variance.md"]
extraction_model: "anthropic/claude-sonnet-4.5"
--- ---
# On Queueing Theory for Large-Scale CI/CD Pipelines Optimization # On Queueing Theory for Large-Scale CI/CD Pipelines Optimization
@ -27,3 +31,10 @@ Academic paper applying classical M/M/c queueing theory to model CI/CD pipeline
Direct parallel: our extract/eval pipeline IS a multi-stage CI/CD-like system. Sources arrive (Poisson-ish), workers process them (variable service times), and queue depth determines throughput. The M/M/c framework gives us closed-form solutions for expected wait times given worker counts. Direct parallel: our extract/eval pipeline IS a multi-stage CI/CD-like system. Sources arrive (Poisson-ish), workers process them (variable service times), and queue depth determines throughput. The M/M/c framework gives us closed-form solutions for expected wait times given worker counts.
Key insight: M/M/c queues show that adding workers has diminishing returns — the marginal improvement of worker N+1 decreases as N grows. This means there's an optimal worker count beyond which additional workers waste compute without meaningfully reducing queue wait times. Key insight: M/M/c queues show that adding workers has diminishing returns — the marginal improvement of worker N+1 decreases as N grows. This means there's an optimal worker count beyond which additional workers waste compute without meaningfully reducing queue wait times.
## Key Facts
- M/M/c queues model systems with Poisson arrivals, exponential service times, and c parallel servers
- The paper addresses bottleneck formation in high-volume shared infrastructure pipelines
- Classical queueing models provide closed-form solutions for expected wait times given arrival rates and worker counts
- The framework integrates theoretical queueing analysis with practical optimization including dynamic scaling and prioritization