{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EBZANJUGOFCTG3DBTMLJVJWAHW","short_pith_number":"pith:EBZANJUG","schema_version":"1.0","canonical_sha256":"207206a6867145336c619b169aa6c03d87e26a7b831fef946bbb35ba46d5d798","source":{"kind":"arxiv","id":"1201.5523","version":1},"attestation_state":"computed","paper":{"title":"The supermarket model with arrival rate tending to one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Graham Brightwell, Malwina Luczak","submitted_at":"2012-01-26T14:10:51Z","abstract_excerpt":"In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\\lambda n$, where $\\lambda = \\lambda (n) \\in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean~1. In this paper, we analyse the behaviour of the supermarket model in a regime where $\\lambda(n)$ tends to~1, and $d(n)$ tends to infinity, as $n \\to \\infty$. For suitable triples $(n,d,\\lambda"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.5523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-26T14:10:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"433d9fabc9a80823259b325e5b4c84b67bfa74ff077433fab1589123cfb43a57","abstract_canon_sha256":"7effba4b4ffdd40a3f5a579c3cb0e3631245f4e442edd6936a38d515a8ac7d54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:46.038725Z","signature_b64":"QZu7UltOxsUGew6Cfk8zi8YTxKhRw6ZljShsP81NQBkLwpLwyFWZkXQVlW7q1sxqmlj+3klAx+DS5bTGpyKvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207206a6867145336c619b169aa6c03d87e26a7b831fef946bbb35ba46d5d798","last_reissued_at":"2026-05-18T04:03:46.038218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:46.038218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The supermarket model with arrival rate tending to one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Graham Brightwell, Malwina Luczak","submitted_at":"2012-01-26T14:10:51Z","abstract_excerpt":"In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\\lambda n$, where $\\lambda = \\lambda (n) \\in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean~1. In this paper, we analyse the behaviour of the supermarket model in a regime where $\\lambda(n)$ tends to~1, and $d(n)$ tends to infinity, as $n \\to \\infty$. For suitable triples $(n,d,\\lambda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5523","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.5523","created_at":"2026-05-18T04:03:46.038292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5523v1","created_at":"2026-05-18T04:03:46.038292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5523","created_at":"2026-05-18T04:03:46.038292+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBZANJUGOFCT","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBZANJUGOFCTG3DB","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBZANJUG","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW","json":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW.json","graph_json":"https://pith.science/api/pith-number/EBZANJUGOFCTG3DBTMLJVJWAHW/graph.json","events_json":"https://pith.science/api/pith-number/EBZANJUGOFCTG3DBTMLJVJWAHW/events.json","paper":"https://pith.science/paper/EBZANJUG"},"agent_actions":{"view_html":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW","download_json":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW.json","view_paper":"https://pith.science/paper/EBZANJUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5523&json=true","fetch_graph":"https://pith.science/api/pith-number/EBZANJUGOFCTG3DBTMLJVJWAHW/graph.json","fetch_events":"https://pith.science/api/pith-number/EBZANJUGOFCTG3DBTMLJVJWAHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW/action/storage_attestation","attest_author":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW/action/author_attestation","sign_citation":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW/action/citation_signature","submit_replication":"https://pith.science/pith/EBZANJUGOFCTG3DBTMLJVJWAHW/action/replication_record"}},"created_at":"2026-05-18T04:03:46.038292+00:00","updated_at":"2026-05-18T04:03:46.038292+00:00"}