{
  "abstract": "We study steady-state queueing control when decisions must be learned from a single persistent operating trajectory: only the implemented action produces data, and the queue is not reset when the action changes. Fixed-event-count cycles yield a direct ratio-of-totals sample-average approximation (SAA) of each action's steady-state cost rate. A Top-K coarse-to-fine search ranks these estimates, retains several promising refinement paths, and concentrates later operation on finer candidate sets, without requiring gradients, convexity, or differentiability. We decompose direct-SAA error into accumulated conditional transient bias and martingale fluctuation. For regenerative queues, a bias-function representation reduces transient effects within contiguous action blocks to boundary terms. Finite-sample stagewise bounds then link estimation accuracy to master-grid identification through guardian retention, and the required queueing and sampling conditions are verified for a persistent-workload M/M/1 implementation. At a common active set, Top-K has a weakly larger guardian margin than Top-1, and an exact-objective example shows Top-1 can discard the optimal refinement branch. Numerical experiments delineate scope rather than universal dominance: Top-K improves terminal identification in the reported LiQUAR and mixed staffing comparisons, while LiQUAR can have lower cumulative learning cost, and GOLiQ is markedly stronger on a smooth benchmark with reliable queueing sensitivities. Direct ranking is therefore best viewed as a complementary method when model-specific gradients are unavailable, inconvenient, or poorly matched to the decision space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26653",
  "author_total": 2,
  "authors": [
    {
      "name": "Mehrdad Nozohour Yazdi"
    },
    {
      "name": "Yiqiang Q. Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f120pef96x1xp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26653",
  "fulltext_url": null,
  "id": "f120pef96x1xp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26653",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1404|Advanced Queuing Theory Analysis"
    ]
  ],
  "openalex": "W7223041302",
  "pdf_url": "https://arxiv.org/pdf/2610.26653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f120pef96x1xp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Direct Sample-Average Learning for Queueing Control: Gradient-Free Top-$K$ Coarse-to-Fine Optimization",
  "title_text": "Direct Sample-Average Learning for Queueing Control: Gradient-Free Top-K Coarse-to-Fine Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/f120pef96x1xp",
  "venue": "arXiv",
  "versions": []
}