{
  "abstract": "In this paper, we prove that a mean system utilization smaller than one is a necessary condition for the feasibility of real-time systems. Such systems are defined as stable. Stable systems have two distinct states: a transient state, followed by a steady-state where the same distribution of response times is repeated infinitely for each task. We prove that the Liu and Layland theorem holds for stable probabilistic real-time systems with implicit deadlines, we provide an analytical approximation of response times for each of those two states and a bound of the instant when a real-time system becomes steady.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: IEEE Transactions on Computers ( Volume: 72, Issue: 1, 01 January 2023)",
  "arxiv": "2609.21760",
  "author_total": 4,
  "authors": [
    {
      "name": "Kevin Zagalo"
    },
    {
      "name": "Yasmina Abdeddaïm"
    },
    {
      "name": "Avner Bar-Hen"
    },
    {
      "name": "Liliana Cucu-Grosjean"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fr564pz6mfzy2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21760",
  "fulltext_url": null,
  "id": "fr564pz6mfzy2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21760",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.21760",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fr564pz6mfzy2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21760",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21760"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems",
  "title_text": "Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/fr564pz6mfzy2",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1109/tc.2022.3211421",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}