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: 2026-03-15*
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Bournassenko's framework provides the theoretical foundation for why queue-state-based scaling works: M/M/c models show that current queue depth and utilization are sufficient statistics for optimal worker allocation when arrivals are Poisson-like. This explains why AIMD's simple heuristics can approach optimality without complex prediction.
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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: 2026-03-15*
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Bournassenko's M/M/c framework extends Little's Law by providing closed-form solutions for the buffer margin required above the theoretical minimum. The paper shows that the optimal worker count is not just λW (from Little's Law) but includes a variance-dependent safety margin that can be calculated analytically from the M/M/c model.
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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: 2026-03-15*
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The paper demonstrates this principle specifically for CI/CD pipelines, showing that large-scale shared infrastructure benefits from pooling effects where the relative safety margin decreases as system size increases. This validates the economies-of-scale claim in a production software context.
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---
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Relevant Notes:
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@ -26,6 +26,12 @@ From the SIAM Review tutorial:
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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.
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### Additional Evidence (confirm)
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*Source: [[2025-04-25-bournassenko-queueing-theory-cicd-pipelines]] | Added: 2026-03-15*
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The paper applies square-root staffing principles to CI/CD pipeline optimization, demonstrating that the theoretical framework translates to practical software systems. The M/M/c analysis confirms that safety capacity should scale as √λ for Poisson arrivals.
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---
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Relevant Notes:
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@ -0,0 +1,48 @@
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{
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"rejected_claims": [
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{
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"filename": "m-m-c-queueing-models-provide-closed-form-solutions-for-ci-cd-pipeline-optimization-because-poisson-arrivals-and-exponential-service-enable-analytical-tractability.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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"filename": "worker-scaling-exhibits-diminishing-returns-in-multi-server-queues-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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"filename": "dynamic-worker-allocation-in-pipelines-requires-balancing-utilization-against-queue-wait-time-because-high-utilization-causes-exponential-delay-growth.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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"filename": "pipeline-bottleneck-formation-is-predictable-from-arrival-rate-and-service-time-distributions-enabling-proactive-capacity-planning.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": 4,
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"kept": 0,
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"fixed": 4,
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"rejected": 4,
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"fixes_applied": [
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"m-m-c-queueing-models-provide-closed-form-solutions-for-ci-cd-pipeline-optimization-because-poisson-arrivals-and-exponential-service-enable-analytical-tractability.md:set_created:2026-03-15",
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"worker-scaling-exhibits-diminishing-returns-in-multi-server-queues-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:set_created:2026-03-15",
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"dynamic-worker-allocation-in-pipelines-requires-balancing-utilization-against-queue-wait-time-because-high-utilization-causes-exponential-delay-growth.md:set_created:2026-03-15",
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"pipeline-bottleneck-formation-is-predictable-from-arrival-rate-and-service-time-distributions-enabling-proactive-capacity-planning.md:set_created:2026-03-15"
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],
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"rejections": [
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"m-m-c-queueing-models-provide-closed-form-solutions-for-ci-cd-pipeline-optimization-because-poisson-arrivals-and-exponential-service-enable-analytical-tractability.md:missing_attribution_extractor",
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"worker-scaling-exhibits-diminishing-returns-in-multi-server-queues-because-marginal-wait-time-reduction-decreases-as-server-count-increases.md:missing_attribution_extractor",
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"dynamic-worker-allocation-in-pipelines-requires-balancing-utilization-against-queue-wait-time-because-high-utilization-causes-exponential-delay-growth.md:missing_attribution_extractor",
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"pipeline-bottleneck-formation-is-predictable-from-arrival-rate-and-service-time-distributions-enabling-proactive-capacity-planning.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": "2026-03-15"
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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: 2026-03-15
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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", "square-root-staffing-principle-achieves-economies-of-scale-in-queueing-systems-by-operating-near-full-utilization-with-manageable-delays.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 +31,9 @@ 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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- Bournassenko published 'On Queueing Theory for Large-Scale CI/CD Pipelines Optimization' on arxiv (2504.18705) in April 2025
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- The paper models CI/CD pipeline stages as M/M/c queues with Poisson arrivals and exponential service times
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- The framework integrates theoretical queueing analysis with practical optimization including dynamic scaling and prioritization
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