{
  "abstract": "In this paper, we study an Erlang-type loss system with energy-constrained servers. Each server is equipped with a finite battery and becomes temporarily unavailable for service when its energy is depleted, entering a charging phase before returning to operation upon full recharge. Customers who arrive to find all servers unavailable are blocked and lost immediately. We characterize the steady-state behavior of this two-dimensional Markov process by extending classical truncation results for Jackson networks to incorporate energy dynamics. This yields a closed-form product-form stationary distribution, from which we derive explicit expressions for the steady-state moments and the blocking probability. Finally, we establish that the corresponding M/G/$k$/$k$ queue with stochastic charging is insensitive to both the service-time and charging-time distributions, depending only on their means. Thus, we extend the insensitivity property of the Erlang loss queue to the stochastic server setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01559",
  "author_total": 3,
  "authors": [
    {
      "name": "Elijah Kulikov"
    },
    {
      "name": "Eliezer Fuentes-Quezada"
    },
    {
      "name": "Jamol Pender"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2zkecn25hjpwv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01559",
  "fulltext_url": null,
  "id": "2zkecn25hjpwv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01559",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1404|Advanced Queuing Theory Analysis"
    ]
  ],
  "openalex": "W7206187873",
  "pdf_url": "https://arxiv.org/pdf/2609.01559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2zkecn25hjpwv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Erlang Loss Model with Energy Constrained Servers",
  "title_text": "Erlang Loss Model with Energy Constrained Servers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/2zkecn25hjpwv",
  "venue": "arXiv",
  "versions": []
}