{"paper":{"title":"Growing open Markovian Jackson networks: Fluid limit and infinite-dimensional Skorokhod problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"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.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guodong Pang, Louis T. Clarke, Ruoyu Wu","submitted_at":"2026-05-16T08:08:33Z","abstract_excerpt":"We study growing open Jackson networks where each station is a single-server queue that follows the first-come first-served discipline with Poisson arrivals and exponentially distributed service times, characterized by node-specific rates. In applying a fluid scaling to the queue-length process, we show that 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 by co"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2e077b81c222fe1c52153b82fdd826bec3fb7150a19b3558d87fd4a11d64bd0c"},"source":{"id":"2605.16868","kind":"arxiv","version":1},"verdict":{"id":"54599425-f5b2-4c07-bf64-c678ee3a6de5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:46:44.297971Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16868/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:18.978305Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:50:42.580855Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.300202Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.376347Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"9fafc548ee3178aaae8d10597cd7f8381dcf9a98b0a1dfa46545e8550f976b77"},"references":{"count":47,"sample":[{"doi":"","year":2005,"title":"S. Banerjee and A. Sankararaman. Ergodicity and steady state analysis for interference queueing networks.arXiv preprint arXiv:2005.13051, 2020","work_id":"db0555ed-d461-4156-997c-d7a79e0a89d5","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"E. Bayraktar, S. Chakraborty, and R. Wu. Graphon mean field systems.The Annals of Applied Probability, 33(5):3587–3619, 2023","work_id":"cec144c7-4150-4fe0-bb05-d970137a421c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"G. Bet, F. Coppini, and F. R. Nardi. Weakly interacting oscillators on dense random graphs.Journal of Applied Probability, 61(1):255–278, 2024","work_id":"cbe085ec-b92a-4672-9e64-f153014ea0ee","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1998,"title":"K. A. Borovkov. Propagation of chaos for queueing networks.Theory of Probability & Its Applications, 42(3):385– 394, 1998","work_id":"1fd10356-5bfd-4a6c-9fe4-fb20631e243b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"A. Budhiraja, D. Mukherjee, and R. Wu. Supermarket model on graphs.The Annals of Applied Probability, 29(3):1740–1777, 2019","work_id":"e346c883-ef8f-4e48-abc0-f6a8680d2f5e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":47,"snapshot_sha256":"325bebd3d343eaa06616cc6cc3e62c9096cd04ed463629a564f4a698bfe54424","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"cd54bb079dc703530295a4d217452e27732e89b62797019be4d465d1402efc73"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}