{
  "abstract": "This study develops an analytical and decision framework for a pooled single-server diagnostic--treatment service receiving both first-time and referred patients. A first-time patient receives diagnosis followed immediately by one of $n$ treatment modes, whereas a referred patient enters directly into the prescribed treatment mode. For the two-treatment case, closed-form probability generating functions characterize the stationary queue-length distribution; for arbitrary $n$, a matrix-geometric representation provides a computational solution. The queueing analysis is then directed to capacity control decisions. The effective load is decomposed into mode-specific workload contributions, yielding a minimum service-rate increment for a prescribed utilization target to show that utilization-equivalent interventions need not be delay-equivalent. This motivates a distribution-aware control based on the stationary probability of severe congestion. Finally, the total cost function shown to be strictly convex, providing a global minimum for restricted one-mode interventions. Analytical results are cross-validated against the Pollaczek--Khintchine relations and discrete-event simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07967",
  "author_total": 3,
  "authors": [
    {
      "name": "Shobha Rani"
    },
    {
      "name": "Rohit Dehru"
    },
    {
      "name": "Raghu Nandan Sengupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16d9ysp1gv3pg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07967",
  "fulltext_url": null,
  "id": "16d9ysp1gv3pg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07967",
  "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": "W7202201228",
  "pdf_url": "https://arxiv.org/pdf/2608.07967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16d9ysp1gv3pg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2608.07967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Capacity Control in a Single-Server Diagnostic--Treatment Queue with Heterogeneous Treatment Modes",
  "title_text": "Capacity Control in a Single-Server Diagnostic--Treatment Queue with Heterogeneous Treatment Modes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/16d9ysp1gv3pg",
  "venue": "arXiv",
  "versions": []
}