{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CYKLQQPWBL5GGDTZ3PZOZQHICG","short_pith_number":"pith:CYKLQQPW","canonical_record":{"source":{"id":"1405.4853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-19T19:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862","abstract_canon_sha256":"1b1a5fa565e58ea6419bb7da50cbf75117192a1bd9e3b3fba901bcd0e6f40e58"},"schema_version":"1.0"},"canonical_sha256":"1614b841f60afa630e79dbf2ecc0e81199f8113cd704c41d1c1154283d71af62","source":{"kind":"arxiv","id":"1405.4853","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4853","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4853v1","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4853","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"CYKLQQPWBL5G","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CYKLQQPWBL5GGDTZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CYKLQQPW","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CYKLQQPWBL5GGDTZ3PZOZQHICG","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-19T19:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862","abstract_canon_sha256":"1b1a5fa565e58ea6419bb7da50cbf75117192a1bd9e3b3fba901bcd0e6f40e58"},"schema_version":"1.0"},"canonical_sha256":"1614b841f60afa630e79dbf2ecc0e81199f8113cd704c41d1c1154283d71af62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:32.833208Z","signature_b64":"cERtt+fXIIuRzPtCOX5nSw4fwDl+EiC/PQjfvfVtbDJAIYy/M/n6gaBxX7yEvS0wzOdYK3lsM8G/vSehTsgrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1614b841f60afa630e79dbf2ecc0e81199f8113cd704c41d1c1154283d71af62","last_reissued_at":"2026-05-18T02:51:32.832634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:32.832634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4853","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gB4pLqluUMQ9zQN93iSyqhmi2LdqRLSxnj9tGDzi+OcXI5kPl3P0IoI7nTzfhNMx/8isKa+bWYEW1isJda6rBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:06:48.046625Z"},"content_sha256":"1cda61dc600f12b80bedadc436bf4caeebe0d54255fc8a7d8a0ba50d9d8a9b73","schema_version":"1.0","event_id":"sha256:1cda61dc600f12b80bedadc436bf4caeebe0d54255fc8a7d8a0ba50d9d8a9b73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CYKLQQPWBL5GGDTZ3PZOZQHICG","target":"graph","payload":{"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":"2014-05-19T19:47:47Z","abstract_excerpt":"We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. 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 corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4853","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhKnz7ZRof2KVLuVJOlQWAmgNdhQf2yWe8DPpZVxjr1ubxvTaCts4jd1204U8w+qYD6r/HR1bS7bBicuZWVxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:06:48.046972Z"},"content_sha256":"050df4ffc28dde7fdb81e503b3b92123e726f4618bcedacacc0edb91b00645c1","schema_version":"1.0","event_id":"sha256:050df4ffc28dde7fdb81e503b3b92123e726f4618bcedacacc0edb91b00645c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/bundle.json","state_url":"https://pith.science/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T16:06:48Z","links":{"resolver":"https://pith.science/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG","bundle":"https://pith.science/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/bundle.json","state":"https://pith.science/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYKLQQPWBL5GGDTZ3PZOZQHICG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CYKLQQPWBL5GGDTZ3PZOZQHICG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b1a5fa565e58ea6419bb7da50cbf75117192a1bd9e3b3fba901bcd0e6f40e58","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-19T19:47:47Z","title_canon_sha256":"71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862"},"schema_version":"1.0","source":{"id":"1405.4853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4853","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4853v1","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4853","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"CYKLQQPWBL5G","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CYKLQQPWBL5GGDTZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CYKLQQPW","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:050df4ffc28dde7fdb81e503b3b92123e726f4618bcedacacc0edb91b00645c1","target":"graph","created_at":"2026-05-18T02:51:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. 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 corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.","authors_text":"Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-19T19:47:47Z","title":"Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4853","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1cda61dc600f12b80bedadc436bf4caeebe0d54255fc8a7d8a0ba50d9d8a9b73","target":"record","created_at":"2026-05-18T02:51:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b1a5fa565e58ea6419bb7da50cbf75117192a1bd9e3b3fba901bcd0e6f40e58","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2014-05-19T19:47:47Z","title_canon_sha256":"71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862"},"schema_version":"1.0","source":{"id":"1405.4853","kind":"arxiv","version":1}},"canonical_sha256":"1614b841f60afa630e79dbf2ecc0e81199f8113cd704c41d1c1154283d71af62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1614b841f60afa630e79dbf2ecc0e81199f8113cd704c41d1c1154283d71af62","first_computed_at":"2026-05-18T02:51:32.832634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:32.832634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cERtt+fXIIuRzPtCOX5nSw4fwDl+EiC/PQjfvfVtbDJAIYy/M/n6gaBxX7yEvS0wzOdYK3lsM8G/vSehTsgrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:32.833208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cda61dc600f12b80bedadc436bf4caeebe0d54255fc8a7d8a0ba50d9d8a9b73","sha256:050df4ffc28dde7fdb81e503b3b92123e726f4618bcedacacc0edb91b00645c1"],"state_sha256":"3da8568bb135391eb15835b2e787384441144e4e8dbd967b19e5ed980a282886"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2Jsfr8LoLjCujjsgPlFqER+7fYPIFp02w/u++a/9TJYl+1tx1BD2OetO1v/ItNGSOkSiyw4I6uKtK0lBsvNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:06:48.048945Z","bundle_sha256":"03cdfacf5edb11c7da9495ec31f46e4969106243c8d983a467a4d2f9b2de1d1a"}}