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  "slug": "processor-sharing-freshness",
  "title": "Small service requirements determine information freshness near saturation",
  "shortTitle": "The shortest jobs set the freshness scale",
  "url": "https://evidencepress.org/releases/processor-sharing-freshness/",
  "oneLine": "In a stationary processor-sharing queue, the lower end of the service distribution determines the heavy-traffic age scale, even when queue populations look identical.",
  "abstract": "For a stationary lossless M/G/1 queue with egalitarian processor sharing, Poisson arrivals and a fixed finite-mean service law, this candidate proves a heavy-traffic limit for the freshest-delivered information age. A service CDF behaving as c x^β near zero produces age exponent β/(β+1), with convergence of every positive moment to an explicit product-power exponential law. A regularly varying extension captures slowly varying factors through an integral-defined scale. Obsolete packets remain in service. The written proof does not require a finite service second moment. Fresh bounded checks and historical simulations have distinct provenance; no finite-load error guarantee, external reproduction or formal verification is claimed.",
  "datePublished": "2026-10-20",
  "dateModified": "2026-10-20",
  "version": "1.0.0-candidate",
  "doi": "10.5281/zenodo.23501620",
  "doiUrl": "https://doi.org/10.5281/zenodo.23501620",
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  "repoUrl": "https://github.com/ipitchford/processor-sharing-freshness",
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  "authors": [
    "Anonymous"
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  "keywords": [
    "age of information",
    "processor sharing",
    "heavy traffic",
    "regular variation",
    "stationary queues"
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    "Lower-end service exponent β produces heavy-traffic age exponent β/(β+1).",
    "All positive moments converge; a finite service second moment is not required.",
    "An integral-defined normalization extends the theorem to regularly varying lower-end CDFs, including slowly varying corrections."
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  "evidencePackage": "Written limit and uniform-integrability proofs, three exact finite rational means, bounded stationary simulation and scale checks. Larger historical simulations are labelled and were not rerun for publication.",
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  "relatedWorks": [
    {
      "citation": "Zachary (2007), A note on insensitivity in stochastic networks.",
      "url": "https://doi.org/10.1239/jap/1175267175",
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