Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add vasilyu1983/AI-Agents-public --skill foundations-queueing-theorygit clone --depth 1 https://github.com/vasilyu1983/AI-Agents-publicWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/vasilyu1983/ai-agents-public/foundations-queueing-theory)<a href="https://agentmods.dev/skills/vasilyu1983/ai-agents-public/foundations-queueing-theory"><img src="https://agentmods.dev/badge/skills/vasilyu1983/ai-agents-public/foundations-queueing-theory/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/vasilyu1983/ai-agents-public/foundations-queueing-theory"><img src="https://agentmods.dev/badge/skills/vasilyu1983/ai-agents-public/foundations-queueing-theory.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector warn
SkillSpector: 1 finding, up to medium
These are SkillSpector’s own severities. On a checked sample its high-severity flags on skills were ~96% false positives — a documented command, a public API, a “never do X” rule — so we show them as a caution to read, not a verdict. Why →
- medium analysis-evasion · line 1 Suspicious Unicode normalization or mixed-script contentFix: Review the flagged content for security risks. Ensure no credentials, secrets, or sensitive data are exposed.
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00051 | $0.07888 |
| Opus 5 | $0.00026 | $0.03944 |
| Sonnet 5 | $0.00010 | $0.01578 |
| Haiku 4.5 | $0.00005 | $0.00789 |
Grade A, and why
foundations-queueing-theory scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 6d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 293 lines — stays where its author put it; the contents beside it link to each section on GitHub.
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 | Wq_1 < Wq_2 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))·(CV²_a+CV²_s)/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]·H_K | Fan-out latency dominated by slowest worker |
What ships with it
19 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
- agents/openai.yaml 333 B
- assets/templates/queueing-theory/01-littles-law.md 3.6 KB
- assets/templates/queueing-theory/02-mm1.md 4.2 KB
- assets/templates/queueing-theory/03-mmc.md 7.8 KB
- assets/templates/queueing-theory/04-mg1-pollaczek-khinchine.md 6.7 KB
- assets/templates/queueing-theory/05-priority-queues.md 8.3 KB
- assets/templates/queueing-theory/06-jackson-networks.md 8.0 KB
- assets/templates/queueing-theory/07-kingman-formula.md 5.2 KB
- assets/templates/queueing-theory/08-bufferbloat.md 5.4 KB
- assets/templates/queueing-theory/09-usl-universal-scalability.md 5.2 KB
- assets/templates/queueing-theory/10-loss-systems-erlang-b.md 5.1 KB
- assets/templates/queueing-theory/11-fork-join-parallel.md 5.5 KB
- assets/templates/queueing-theory/README.md 4.9 KB
- data/sources.json 18 KB
- learnings.consolidated.md 603 B
- learnings.md 1.0 KB
- references/formal-theory-map.md 3.3 KB
- references/patterns-scenarios-traps.md 2.9 KB
- references/primitives-overview.md 7.8 KB
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 6d ago First seen · 293 lines · 51 tokens per session scan A e643c8251da4
foundations-queueing-theory is a skill published in the GitHub repository vasilyu1983/AI-Agents-public (87 stars, last pushed 7d ago), licensed MIT. It adds 51 tokens to every session and 7,888 once invoked, about $0.0003 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.
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