Pith Number

pith:D5RZCSR6

pith:2026:D5RZCSR6YXNSOEKYWYMULGLKEJ

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Growing open Markovian Jackson networks: Fluid limit and infinite-dimensional Skorokhod problem

Guodong Pang, Louis T. Clarke, Ruoyu Wu

Under suitable growth conditions, open Jackson networks converge in the fluid scale to the unique solution of an infinite-dimensional Skorokhod problem with a kernel reflection operator.

arxiv:2605.16868 v1 · 2026-05-16 · math.PR

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Record completeness

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4 Citations open

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Claims

C1strongest claim

Under certain conditions the queueing system can be approximated by an infinite-dimensional fluid limit with a kernel function in place of the transition matrix. This limiting process can be characterized by an infinite-dimensional Skorokhod problem, for which we develop a new theory... We establish existence and uniqueness of a solution along with Lipschitz continuity provided the reflecting operator has a spectral radius less than 1.

C2weakest assumption

The network growth and rate conditions allow the reflection operator to satisfy a spectral radius strictly less than 1, which is required for the Lipschitz property of the infinite-dimensional Skorokhod mapping and for the convergence arguments via the intermediate process and martingale estimates.

C3one line summary

Proves fluid limits for growing open Markovian Jackson networks via a new theory of infinite-dimensional Skorokhod problems with existence, uniqueness, and Lipschitz continuity under a spectral radius condition.

References

47 extracted · 47 resolved · 0 Pith anchors

[1] S. Banerjee and A. Sankararaman. Ergodicity and steady state analysis for interference queueing networks.arXiv preprint arXiv:2005.13051, 2020 2005

[2] E. Bayraktar, S. Chakraborty, and R. Wu. Graphon mean field systems.The Annals of Applied Probability, 33(5):3587–3619, 2023 2023

[3] G. Bet, F. Coppini, and F. R. Nardi. Weakly interacting oscillators on dense random graphs.Journal of Applied Probability, 61(1):255–278, 2024 2024

[4] K. A. Borovkov. Propagation of chaos for queueing networks.Theory of Probability & Its Applications, 42(3):385– 394, 1998 1998

[5] A. Budhiraja, D. Mukherjee, and R. Wu. Supermarket model on graphs.The Annals of Applied Probability, 29(3):1740–1777, 2019 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:27.320367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f63914a3ec5db271158b61945996a2264f565f7ddf64258d75f540e0e0d0c78

Aliases

arxiv: 2605.16868 · arxiv_version: 2605.16868v1 · doi: 10.48550/arxiv.2605.16868 · pith_short_12: D5RZCSR6YXNS · pith_short_16: D5RZCSR6YXNSOEKY · pith_short_8: D5RZCSR6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D5RZCSR6YXNSOEKYWYMULGLKEJ \
  | 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: 1f63914a3ec5db271158b61945996a2264f565f7ddf64258d75f540e0e0d0c78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "273aa0a1d8b755e9af524b091736969e630d0fe83458b1a3267ebfcb217ca4ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-16T08:08:33Z",
    "title_canon_sha256": "99fc3643d1567d6d847ffa9c0f5d963dee3dc990550fc175a56138cdf4ca6ebb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16868",
    "kind": "arxiv",
    "version": 1
  }
}