{
  "abstract": "Real-time services, such as VoIP and large-scale neural network training, require strict transmission delay guarantees. While routing under hop constraints is tractable, real-world delays increase sharply with equipment load, typically modeled using the M/M/1 queuing function where delay is inversely proportional to available bandwidth. We investigate the resulting Delay-Constrained Maximum Concurrent Flow (DCMCF) problem, which seeks to maximize the minimum throughput across all commodities. The problem's complexity stems from the conditional and non-linear nature of the delay constraints, which are active only along the specific paths used by the flow. We prove that DCMCF is strongly NP-hard, even for single-source/single-destination instances. To address the inherent non-convexity of the problem, we introduce a new convex relaxation expressed through second-order cone constraints, obtained from the convex envelope of a function representing the conditional delay associated with a single arc of a given path. The relaxation is shown to outperform existing formulations based on disjunctive programming. Leveraging this result, we develop a polynomial-time approximation algorithm with a provable performance guarantee and present numerical experiments demonstrating the effectiveness of the proposed approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05068",
  "author_total": 4,
  "authors": [
    {
      "name": "Walid Ben-Ameur"
    },
    {
      "name": "Guillaume Beraud-Sudreau"
    },
    {
      "name": "Hervé Kerivin"
    },
    {
      "name": "Sebastien Martin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wmd1g4j8vgv2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05068",
  "fulltext_url": null,
  "id": "5wmd1g4j8vgv2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05068",
  "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.NI"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7211897682",
  "pdf_url": "https://arxiv.org/pdf/2609.05068",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wmd1g4j8vgv2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05068",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05068"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the Delay-Constrained Maximum Concurrent Flow Problem",
  "title_text": "On the Delay-Constrained Maximum Concurrent Flow Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/5wmd1g4j8vgv2",
  "venue": "arXiv",
  "versions": []
}