extract: 2025-04-25-bournassenko-queueing-theory-cicd-pipelines
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Teleo Agents
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@ -31,6 +31,12 @@ For the Teleo pipeline specifically: when extract produces claims faster than ev
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The tradeoff: AIMD is reactive rather than predictive, so it responds to load changes rather than anticipating them. For bursty workloads with predictable patterns, ML-based prediction might provision capacity faster. But for unpredictable workloads or systems where prediction accuracy is low, AIMD's simplicity and guaranteed stability are compelling.
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### Additional Evidence (extend)
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*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
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M/M/c queueing models provide theoretical foundation for why queue-state-based scaling works: closed-form solutions exist for wait times given arrival rates and server counts, meaning optimal worker allocation can be computed from observable queue depth without predicting future load.
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---
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Relevant Notes:
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@ -28,6 +28,12 @@ For Teleo pipeline: if processing ~8 sources per extraction cycle (every 5 min)
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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.
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### Additional Evidence (extend)
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*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
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M/M/c queueing theory provides closed-form solutions for expected wait times given worker counts, enabling precise capacity planning beyond Little's Law's minimum floor. The framework connects arrival rate modeling to worker count optimization through explicit formulas that account for variance.
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---
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Relevant Notes:
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@ -27,6 +27,12 @@ Ward Whitt presents this as a fundamental result from multi-server queueing anal
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This is observable in practice across industries: Amazon's fulfillment centers, telecom networks, and financial trading systems all exhibit this scaling behavior.
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### Additional Evidence (confirm)
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*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-16*
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M/M/c queue analysis demonstrates that the marginal improvement of worker N+1 decreases as N grows, providing mathematical proof that safety margins scale sublinearly. This is a fundamental property of multi-server queues, not just an empirical observation.
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---
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Relevant Notes:
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@ -0,0 +1,26 @@
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{
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"rejected_claims": [
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{
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"filename": "m-m-c-queue-worker-scaling-exhibits-diminishing-returns-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md",
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"issues": [
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"missing_attribution_extractor"
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]
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}
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],
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"validation_stats": {
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"total": 1,
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"kept": 0,
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"fixed": 3,
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"rejected": 1,
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"fixes_applied": [
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"m-m-c-queue-worker-scaling-exhibits-diminishing-returns-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:set_created:2026-03-16",
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"m-m-c-queue-worker-scaling-exhibits-diminishing-returns-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:stripped_wiki_link:multi-server-queueing-systems-exhibit-economies-of-scale-bec",
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"m-m-c-queue-worker-scaling-exhibits-diminishing-returns-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:stripped_wiki_link:square-root-staffing-principle-achieves-economies-of-scale-i"
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],
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"rejections": [
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"m-m-c-queue-worker-scaling-exhibits-diminishing-returns-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:missing_attribution_extractor"
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]
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},
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"model": "anthropic/claude-sonnet-4.5",
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"date": "2026-03-16"
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}
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@ -6,8 +6,12 @@ url: https://arxiv.org/abs/2504.18705
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date: 2025-04-25
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domain: internet-finance
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format: paper
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status: unprocessed
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status: enrichment
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tags: [pipeline-architecture, operations-research, queueing-theory, ci-cd, M/M/c-queue]
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processed_by: rio
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processed_date: 2026-03-16
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enrichments_applied: ["littles-law-provides-minimum-worker-capacity-floor-for-pipeline-systems-but-requires-buffer-margin-for-variance.md", "multi-server-queueing-systems-exhibit-economies-of-scale-because-safety-margin-grows-sublinearly-with-system-size.md", "aimd-worker-scaling-requires-only-queue-state-observation-not-load-prediction-making-it-simpler-than-ml-based-autoscaling.md"]
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extraction_model: "anthropic/claude-sonnet-4.5"
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---
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# On Queueing Theory for Large-Scale CI/CD Pipelines Optimization
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@ -27,3 +31,10 @@ Academic paper applying classical M/M/c queueing theory to model CI/CD pipeline
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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.
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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.
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## Key Facts
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- M/M/c queues model Poisson arrivals, exponential service times, and c servers
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- Classical queueing theory provides closed-form solutions for expected wait times in multi-server systems
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- The paper addresses bottleneck formation in high-volume shared infrastructure pipelines
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- Framework integrates theoretical queueing analysis with practical optimization for dynamic scaling
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