{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KAQXP2JDXFMU3NWYAYQF4C7R3M","short_pith_number":"pith:KAQXP2JD","schema_version":"1.0","canonical_sha256":"502177e923b9594db6d806205e0bf1db00f27d0394a54627ebf0f26e048fc111","source":{"kind":"arxiv","id":"1104.3192","version":2},"attestation_state":"computed","paper":{"title":"On Large Delays in Multi-Server Queues with Heavy Tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitry Korshunov, Sergey Foss","submitted_at":"2011-04-16T03:44:09Z","abstract_excerpt":"We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\\rho$ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a `principle of $s-k$ big jumps' in this case (here $k$ is the integer part of $\\rho$), which gives the most probable way for the stationary waiting time to be large.\n  Another corollary of the bounds obta"},"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":"1104.3192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-16T03:44:09Z","cross_cats_sorted":[],"title_canon_sha256":"4764c705e91b111ab9675105d8356ee0c992ce264a787cf91aac76d578c764a8","abstract_canon_sha256":"984ace98718a076bdcbd0b32400d895f08b5ec81c68c2b821f50d755231cadd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:28.345693Z","signature_b64":"YHoxIhXHAiSQq75PwXBuyt8f/X4kHX3LdVNIZGkhSyQVgN+wi18qiE1leBGZ9A0caZF5FsN8alZUbOCu/0lKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"502177e923b9594db6d806205e0bf1db00f27d0394a54627ebf0f26e048fc111","last_reissued_at":"2026-05-18T03:30:28.344796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:28.344796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Large Delays in Multi-Server Queues with Heavy Tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitry Korshunov, Sergey Foss","submitted_at":"2011-04-16T03:44:09Z","abstract_excerpt":"We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\\rho$ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a `principle of $s-k$ big jumps' in this case (here $k$ is the integer part of $\\rho$), which gives the most probable way for the stationary waiting time to be large.\n  Another corollary of the bounds obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3192","kind":"arxiv","version":2},"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":"1104.3192","created_at":"2026-05-18T03:30:28.344936+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3192v2","created_at":"2026-05-18T03:30:28.344936+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3192","created_at":"2026-05-18T03:30:28.344936+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAQXP2JDXFMU","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAQXP2JDXFMU3NWY","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAQXP2JD","created_at":"2026-05-18T12:26:32.869790+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/KAQXP2JDXFMU3NWYAYQF4C7R3M","json":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M.json","graph_json":"https://pith.science/api/pith-number/KAQXP2JDXFMU3NWYAYQF4C7R3M/graph.json","events_json":"https://pith.science/api/pith-number/KAQXP2JDXFMU3NWYAYQF4C7R3M/events.json","paper":"https://pith.science/paper/KAQXP2JD"},"agent_actions":{"view_html":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M","download_json":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M.json","view_paper":"https://pith.science/paper/KAQXP2JD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3192&json=true","fetch_graph":"https://pith.science/api/pith-number/KAQXP2JDXFMU3NWYAYQF4C7R3M/graph.json","fetch_events":"https://pith.science/api/pith-number/KAQXP2JDXFMU3NWYAYQF4C7R3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M/action/storage_attestation","attest_author":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M/action/author_attestation","sign_citation":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M/action/citation_signature","submit_replication":"https://pith.science/pith/KAQXP2JDXFMU3NWYAYQF4C7R3M/action/replication_record"}},"created_at":"2026-05-18T03:30:28.344936+00:00","updated_at":"2026-05-18T03:30:28.344936+00:00"}