{
  "abstract": "Mobility in three-dimensional (3D) cellular networks induces frequent handovers and random sojourn times for aerial users. Analyzing these events is challenging because they jointly depend on user trajectories and random service-boundary geometry. This paper develops a unified geometric--kinematic framework in which service regions form a stationary random tessellation, their boundaries constitute a random closed set, and user motion follows a cruise--turn mobility model. Under the stated stationarity, isotropy, and independence conditions, the handover rate satisfies the exact law \\(H=(S_V/2)\\bar v\\), where \\(S_V\\) is the specific surface area and \\(\\bar v\\) is the long-run mean speed. The forward boundary-distance distribution provides the local geometric input to an effective-traversal approximation for the mean remaining sojourn time. These results link global and local geometric descriptors to complementary mobility metrics. Combining the handover law with link coverage yields a handover-aware effective spectral efficiency for base station (BS) density selection and service-architecture comparison. We then specialize the framework to Poisson--Voronoi single-BS service and Poisson--Delaunay four-BS coordinated multi-point service; under both models, the handover rate scales as \\(λ^{1/3}\\bar v\\). Numerical results corroborate the exact handover expressions, assess the sojourn-time approximations, and show how user speed and interruption duration affect the preferred density and architecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23075",
  "author_total": 2,
  "authors": [
    {
      "name": "Tian Shi"
    },
    {
      "name": "Minghua Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c98datzexb8d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23075",
  "fulltext_url": null,
  "id": "9c98datzexb8d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23075",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.23075",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c98datzexb8d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23075",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23075"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Unified Geometric--Kinematic Laws of Mobility in 3D Cellular Networks",
  "title_text": "Unified Geometric--Kinematic Laws of Mobility in 3D Cellular Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/9c98datzexb8d",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1109/twc.2026.3743548",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}