Agent skill · vasilyu1983
foundations-queueing-theory
Applies queueing theory (Little's Law, M/M/c, Erlang, Kingman, USL) to capacity and latency decisions. Use when load causes non-linear latency growth or queue overrun risk.
What it needs
About 11k tokens when loaded.
What this skill does
Queueing Theory Foundations 11 queueing-theory primitives for capacity planning, saturation prediction, and backpressure design. Each primitive addresses a specific failure mode that causes systems to degrade, saturate, or scale incorrectly. Primitives are domain-agnostic: the same M/M/c formula that sizes a call-center agent pool also sizes a database connection pool and a Kubernetes pod replica count. Contents Quick Reference Primitive Index Formal Supporting Theory Misuse Boundaries Expert Judgment Decision Checklist Anti-Patterns Composition Recipes Workflow ASCII Flow Related Skills Navigation Fact-Checking --- Quick Reference # Primitive Formula / Key Result Use When --- ----------- --------------------- ---------- 1 Little's Law L = λW Relating queue depth, rate, and latency at any stable system 2 M/M/1 W = 1/(μ−λ) Single-server baseline; understanding saturation curve 3 M/M/c (Erlang-C) C(c,a) Erlang-C formula Multi-server pool sizing; wait-time SLO compliance 4 M/G/1 / Pollaczek-Khinchine Wq = ρ·E[S]·(1+CV²)/2(1−ρ) Service-time variability inflating queue latency 5 Priority Queues Wq1 < Wq2 via P-K residual Protecting high-priority workloads from low-priority batch 6 Jackson Networks Product-form: π = Πᵢ πᵢ Multi-stage pipeline bottleneck identification 7 Kingman's Formula Wq ≈ (ρ/(1−ρ))·(CV²a+CV²s)/2·E[S] G/G/1 under real bursty+variable traffic 8 Bufferbloat Buffer > BDP → standing queue Diagnosing high latency despite good throughput 9 USL X(N) = λN/(1+σ(N−1)+κN(N−1)) Predicting retrograde throughput when scaling out 10 Erlang-B (Loss) B(c,a) blocking formula Sizing channels/connections for drop-on-busy systems 11 Fork-Join E[max] = E[S]·HK Fan-out latency dominated by slowest worker --- When to Apply Apply queueing-theory when: Latency at p95/p99 grows non-linearly with load (sign of utilisation > 0.7) Queue or buffer can fill faster than it drains (request queue, message broker, thread pool) Capacity planning: "how many servers/replicas/workers do we n …
How to use it
Reference it in AdaL, Claude Code, Cursor or any coding agent — nothing to install:
@skills vasilyu1983/foundations-queueing-theory