{
  "abstract": "Edge–cloud task scheduling reserves uplink capacity before the wireless service state is known. The reserve depends on both the probability law over a prescribed service-state library and the geometry representing that library. This study separates and quantifies these two effects in a fixed-workload finite-state model. We eliminate post-state bandwidth–CPU recourse exactly, derive a quadratic capacity representation in inverse-square-root spectral efficiencies, and compare empirical (EMP), Wasserstein, hard-support (HARD), and rectangular (BOX) uncertainty models under schedule reoptimization. The analysis yields an exact support-rectangularization premium, a resource-weighted joint-extreme deficit with a relative-cost factor below two, a sandwich bound on the optimized premium, and a finite hardening radius for chance-constrained capacity. Across 60 instances, mean savings from retaining joint support are 6.45–9.32% relative to rectangular protection. Across 20 instances, mean relative increases are 7.39–10.82% for EMP-to-HARD, 8.80–9.26% for support rectangularization, and 16.98–20.89% for EMP-to-BOX; all are deterministic optimization bounds. Positive lower bounds persist for both changed-target workloads, all nine nested-support cases, and both probability-side variations, while intermediate Wasserstein capacity changes under the alternative transport metric. Probability protection and support geometry impose distinct, quantifiable capacity costs.",
  "abstract_shown": true,
  "affiliations": [
    "School of Computer Science and Engineering, Yeungnam University, Gyeongsan 38541, Republic of Korea",
    "Department of Information and Communication Engineering, Yeungnam University, Gyeongsan 38541, Republic of Korea"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mikail Mohammed Salim",
      "orcid": "0000-0001-7870-9368"
    },
    {
      "affs": [
        1
      ],
      "name": "Farheen Naaz",
      "orcid": "0009-0005-5717-5287"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cp1gxdhp0z0j.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203821",
  "fulltext_url": null,
  "id": "4cp1gxdhp0z0j",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3821",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1705|IoT and Edge/Fog Computing"
    ]
  ],
  "openalex": "W7223056876",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/4cp1gxdhp0z0j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203821",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling",
  "title_text": "Capacity Costs of Probability Ambiguity and Support Rectangularization in Edge–Cloud Scheduling",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/4cp1gxdhp0z0j",
  "venue": "Mathematics",
  "versions": []
}