{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2APHYMNTBNEMLOFQNYYFBKU5Y3","short_pith_number":"pith:2APHYMNT","schema_version":"1.0","canonical_sha256":"d01e7c31b30b48c5b8b06e3050aa9dc6c2f0fda351428662f5554e707b8c8fef","source":{"kind":"arxiv","id":"1405.0138","version":1},"attestation_state":"computed","paper":{"title":"Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou","submitted_at":"2014-05-01T11:42:40Z","abstract_excerpt":"Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a bounded relative error. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive our approximations as a sum of the workload distribution of th"},"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":"1405.0138","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-01T11:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862","abstract_canon_sha256":"5e02a4bbc827a3e375c10c7e304cf1a85968fcdac6756c8944b5e549afedee41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:48.911756Z","signature_b64":"uU0iJG5s3PeGWMz1FdUzUca6bOTa2v5/w1briG8+rQV6o2oNwZUSDnOWcKpXndSkB7isNQVs0+LGp+APtN6WBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d01e7c31b30b48c5b8b06e3050aa9dc6c2f0fda351428662f5554e707b8c8fef","last_reissued_at":"2026-05-18T02:52:48.911232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:48.911232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou","submitted_at":"2014-05-01T11:42:40Z","abstract_excerpt":"Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a bounded relative error. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive our approximations as a sum of the workload distribution of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0138","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":"1405.0138","created_at":"2026-05-18T02:52:48.911313+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.0138v1","created_at":"2026-05-18T02:52:48.911313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0138","created_at":"2026-05-18T02:52:48.911313+00:00"},{"alias_kind":"pith_short_12","alias_value":"2APHYMNTBNEM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2APHYMNTBNEMLOFQ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2APHYMNT","created_at":"2026-05-18T12:28:09.283467+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/2APHYMNTBNEMLOFQNYYFBKU5Y3","json":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3.json","graph_json":"https://pith.science/api/pith-number/2APHYMNTBNEMLOFQNYYFBKU5Y3/graph.json","events_json":"https://pith.science/api/pith-number/2APHYMNTBNEMLOFQNYYFBKU5Y3/events.json","paper":"https://pith.science/paper/2APHYMNT"},"agent_actions":{"view_html":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3","download_json":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3.json","view_paper":"https://pith.science/paper/2APHYMNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.0138&json=true","fetch_graph":"https://pith.science/api/pith-number/2APHYMNTBNEMLOFQNYYFBKU5Y3/graph.json","fetch_events":"https://pith.science/api/pith-number/2APHYMNTBNEMLOFQNYYFBKU5Y3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3/action/storage_attestation","attest_author":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3/action/author_attestation","sign_citation":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3/action/citation_signature","submit_replication":"https://pith.science/pith/2APHYMNTBNEMLOFQNYYFBKU5Y3/action/replication_record"}},"created_at":"2026-05-18T02:52:48.911313+00:00","updated_at":"2026-05-18T02:52:48.911313+00:00"}