{
  "schema_version": 1,
  "problem_number": "AIM-PROBABILITY-0027",
  "title": "Explicit Stationary Comparisons for Join-the-Shortest-Queue Approximations",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We compare the stationary occupancy law of a finite join-the-shortest-queue system with its finite-buffer and sampled-routing approximations. For N unit-rate exponential servers, Poisson arrival rate 0<lambda<N and rho=lambda/N, regeneration gives H=((1-rho)^(-N)-1)/lambda. With capacity b and blocking probability B_b, the total variation error is at most lambda H(bN+1)B_b. Explicit upper and lower bounds prove sharp order lambda^(bN+1) as lambda tends to zero for fixed N,b. For shortest-of-k routing we obtain explicit total variation bounds for both sampling conventions. These estimates answer the two comparison requests in AIM Problem 1.35 for every bounded occupancy observable. Constants can be loose or trivial at high load or large N; no sharp many-server approximation is asserted.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.PR"
  ],
  "keywords": [
    "join-the-shortest-queue",
    "total variation",
    "finite buffers",
    "power-of-k routing",
    "Stein method",
    "light traffic",
    "AIM-PROBABILITY-0027",
    "math.PR"
  ],
  "manuscript_version_date": "2026-09-28",
  "publication_date": "2026-09-28",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-28",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-probability-0027/",
  "pdf_url": "https://eulersolve.org/papers/aim-probability-0027/paper.pdf?v=65bb3cf17912",
  "doi": "10.5281/zenodo.23024007",
  "zenodo_record_url": "https://zenodo.org/records/23024007",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of the stated finite-N, bounded-observable comparisons, not a claim to close every interpretation of the open-ended source programme. Constants may be trivial at high load or large N. No sharp many-server rate, unbounded-test estimate or exact light-traffic leading coefficient is asserted. Classical weak majorization, regeneration, Ma-Maguluri hitting-time induction and generator comparison are credited. Self-audited and unrefereed; no independent certification, formal verification or absolute priority. Folklore or unlocated prior art is not excluded.",
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    "source.zip": {
      "sha256": "737546aa5979d7651b725f815f15294f2a12a605086c9e8c50a79c0f8d255a14"
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    "verification_report.md": {
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  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}