{
  "abstract": "We construct finite-state Markov arrival-rate processes for which faster modulation increases the mean stationary workload of a stable single-server queue, disproving the universal ordering in Leskelä's formulation of Ross's second conjecture. A 64-state example has positive transition rates between every pair of states, independent service times uniform on $[0.99,1.01]$, and an explicit positive workload gap. A 128-state example additionally has strictly positive arrival-rate autocovariance at every lag. More generally, finite-state examples can exhibit any prescribed finite number of separated workload rises and falls. The proofs use a second-order expansion with a nonnegative, speed-uniform remainder under only a finite second service moment. We characterize the service distributions for which the second-order workload coefficient is nonincreasing for every bounded stationary environment: the function $s\\mapsto\\mathbb{E}(1-\\cos(sB))/s^2$ must be nonincreasing. Mixtures of exponential service distributions satisfy this criterion. An exact Palm identity transfers the workload reversals to customer waiting times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25084",
  "author_total": 1,
  "authors": [
    {
      "name": "Yitzchak Shmalo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb2tbmxcatscg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25084",
  "fulltext_url": null,
  "id": "cb2tbmxcatscg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25084",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1404|Advanced Queuing Theory Analysis"
    ]
  ],
  "openalex": "W7214077967",
  "pdf_url": "https://arxiv.org/pdf/2609.25084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb2tbmxcatscg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Finite-state counterexamples to Ross's second queueing conjecture",
  "title_text": "Finite-state counterexamples to Ross's second queueing conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/cb2tbmxcatscg",
  "venue": "arXiv",
  "versions": []
}