{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:K4HOZQU3NWXY2EGJC7JANBYRAO","short_pith_number":"pith:K4HOZQU3","schema_version":"1.0","canonical_sha256":"570eecc29b6daf8d10c917d2068711038521784b1c0da93e08018d91d175f83f","source":{"kind":"arxiv","id":"1308.2444","version":1},"attestation_state":"computed","paper":{"title":"Poisson's equation for discrete-time quasi-birth-and-death processes","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guy Latouche, Sarah Dendievel, Yuanyuan Liu","submitted_at":"2013-08-12T01:44:05Z","abstract_excerpt":"We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix.\n  We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value."},"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":"1308.2444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2013-08-12T01:44:05Z","cross_cats_sorted":[],"title_canon_sha256":"13626537aadc3ec537777ce5eeba838f67d4dad6c916904bb4b3bafc009f5009","abstract_canon_sha256":"ea71f00512ffa115d16199b161feed67257fe2b9d13d2294f5056127717ae86d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:07.385618Z","signature_b64":"ppJCsQMztdMMPrjlQt29JwricxOfNaewheda6muQ2NEiYfL8RiOhDjaa3YMUXO0f4kjUruhtVsGlcToikA7MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"570eecc29b6daf8d10c917d2068711038521784b1c0da93e08018d91d175f83f","last_reissued_at":"2026-05-18T03:16:07.385046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:07.385046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson's equation for discrete-time quasi-birth-and-death processes","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guy Latouche, Sarah Dendievel, Yuanyuan Liu","submitted_at":"2013-08-12T01:44:05Z","abstract_excerpt":"We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix.\n  We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2444","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":"1308.2444","created_at":"2026-05-18T03:16:07.385142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2444v1","created_at":"2026-05-18T03:16:07.385142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2444","created_at":"2026-05-18T03:16:07.385142+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4HOZQU3NWXY","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4HOZQU3NWXY2EGJ","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4HOZQU3","created_at":"2026-05-18T12:27:49.015174+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/K4HOZQU3NWXY2EGJC7JANBYRAO","json":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO.json","graph_json":"https://pith.science/api/pith-number/K4HOZQU3NWXY2EGJC7JANBYRAO/graph.json","events_json":"https://pith.science/api/pith-number/K4HOZQU3NWXY2EGJC7JANBYRAO/events.json","paper":"https://pith.science/paper/K4HOZQU3"},"agent_actions":{"view_html":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO","download_json":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO.json","view_paper":"https://pith.science/paper/K4HOZQU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2444&json=true","fetch_graph":"https://pith.science/api/pith-number/K4HOZQU3NWXY2EGJC7JANBYRAO/graph.json","fetch_events":"https://pith.science/api/pith-number/K4HOZQU3NWXY2EGJC7JANBYRAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO/action/storage_attestation","attest_author":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO/action/author_attestation","sign_citation":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO/action/citation_signature","submit_replication":"https://pith.science/pith/K4HOZQU3NWXY2EGJC7JANBYRAO/action/replication_record"}},"created_at":"2026-05-18T03:16:07.385142+00:00","updated_at":"2026-05-18T03:16:07.385142+00:00"}