{
  "abstract": "We consider a system of $N$ parallel, homogeneous servers, each with finite capacity $C$. Jobs requiring one unit of capacity arrive according to a Poisson process with total rate $Nλ$ and have exponential service times with rate $μ$. We study a decentralized random--retrial policy with $d$ attempts: upon arrival, a job is assigned to a uniformly chosen server; if the server is full, the job is reassigned to another uniformly chosen server, for at most $d$ attempts; if all $d$ attempts fail, the job is rejected. In the mean-field limit, we prove that the stationary blocking probability is characterized by the unique solution of a fixed-point equation involving the Erlang-B loss function, and we establish global convergence of the fluid model to this equilibrium. We also compare the mean-field stationary blocking probability with the analogous quantity in the power-of-$d$ model under the same parameters $(C,λ,μ)$. For the same $d$, we show, via coupling techniques, that the blocking probability under power-of-$d$ is always less than or equal to the blocking under retrial-of-$d$; but if we consider $d$ and $\\tilde d$ with $\\tilde d>d$, then the retrial-of-$\\tilde d$ policy achieves a strictly lower blocking than the power-of-$d$ policy when $ρ=λ/μ$ is sufficiently large. Moreover we show that for some specific cases, like $C=2$, $d=2$ and $\\tilde d=3$, it occurs for all $ρ>0$, not only for $ρ$ sufficiently large. We complement the analysis with simulations that estimate the load level above which retrial-of-$\\tilde d$ outperforms power-of-$d$ in terms of blocking.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06267",
  "author_total": 4,
  "authors": [
    {
      "name": "D Cuesta"
    },
    {
      "name": "M Jonckheere"
    },
    {
      "name": "B J Prabhu"
    },
    {
      "name": "O Brun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/865stz45rq42y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06267",
  "fulltext_url": null,
  "id": "865stz45rq42y",
  "issns": [],
  "landing_url": "https://hal.science/hal-05852014v1",
  "language": "en",
  "licence": "LicenseRef-publisher-terms",
  "licence_label": "Publisher terms",
  "licence_source": "article",
  "licence_url": "https://hal.science/licences/copyright/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05852014/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/865stz45rq42y.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:20:13Z",
      "native_id": "hal-05852014",
      "source": "hal",
      "url": "https://hal.science/hal-05852014v1"
    },
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06267"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Retrials in Loss Systems: Mean-Field Analysis, Erlang Bounds, and Power-of-d Comparison",
  "title_text": "Retrials in Loss Systems: Mean-Field Analysis, Erlang Bounds, and Power-of-d Comparison",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/865stz45rq42y",
  "venue": "HAL",
  "versions": []
}