Pith Number

pith:JRKA7AVZ

pith:2026:JRKA7AVZGRDP3BY74QFOI25NV3

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Rank Based Routing in Large Server Systems under Extreme Congestion

Amarjit Budhiraja, Eva Loeser, Sayan Banerjee

Marginal join-the-shortest-queue routing drives ranked queue gaps to a reflected Atlas process with explicit product-form stationary laws under extreme heavy traffic.

arxiv:2605.17677 v1 · 2026-05-17 · math.PR

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Claims

C1strongest claim

Under diffusive scaling the ranked queue lengths and associated gap process converge to an infinite-dimensional reflected Atlas process with reflection at the origin and rank-based drift acting on the lowest particle; this limit admits a one-parameter family of product-form stationary gap distributions parametrized by a and b.

C2weakest assumption

The auxiliary 'system with pauses' agrees with the original queueing dynamics at diffusion scale and admits an exact open Jackson network representation whose stationary distributions, when taken to heavy traffic, select the product-form invariants of the reflected Atlas process.

C3one line summary

Proves diffusion limits for ranked queue lengths under marginal JSQ routing in extreme heavy traffic, yielding a reflected Atlas process with explicit product-form stationary gap distributions and sharp asymptotics for imbalance and delay.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Rami Atar,A diffusion regime with nondegenerate slowdown, Operations Research60(2012), no. 2, 490–500 2012

[2] Rami Atar and Tomoyuki Ichiba,Rank-based stochastic differential inclusions and diffusion limits for a load-balancing model, Mathematics of Operations Research (2025) 2025

[3] Rami Atar and Gershon Wolansky,Invariance principle and Mckean–Vlasov limit for ran- domized load balancing in heavy traffic, The Annals of Applied Probability35(2025), no. 5, 3046–3085 2025

[4] Sayan Banerjee and Amarjit Budhiraja,Domains of attraction of invariant distributions of the infinite Atlas model, Annals of Probability50(2022), no. 6, 2286–2339 2022

[5] Sayan Banerjee and Amarjit Budhiraja,Extremal invariant distributions of infinite brownian particle systems with rank dependent drifts, Probability Theory and Related Fields190(2024), no. 1, 79–117 2024

Receipt and verification

First computed	2026-05-20T00:04:52.241729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c540f82b93446fd871fe40ae46badaef85c5be96003f60d6a1559de85318945

Aliases

arxiv: 2605.17677 · arxiv_version: 2605.17677v1 · doi: 10.48550/arxiv.2605.17677 · pith_short_12: JRKA7AVZGRDP · pith_short_16: JRKA7AVZGRDP3BY7 · pith_short_8: JRKA7AVZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JRKA7AVZGRDP3BY74QFOI25NV3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4c540f82b93446fd871fe40ae46badaef85c5be96003f60d6a1559de85318945

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f112ffdaeb92fa629061720742e3004ecfb54a258a6def316117994cf323fd4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-17T22:16:41Z",
    "title_canon_sha256": "04c6bc8ffa385259898115f420b063b93e09fee2527ed933ea845b80f5137789"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
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}