{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VTQSKI6HY7QIIFRDHRGND2LNLM","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":"4705deff40c4d001ce1d3d7a6552537286e8ff9a97336ba910099e93a52712a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-03T14:18:03Z","title_canon_sha256":"199877c814a2ccc2ece9a0718d4735df045de32a26e88e195a16a23939dd2093"},"schema_version":"1.0","source":{"id":"1804.00984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00984","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00984v2","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00984","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"VTQSKI6HY7QI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTQSKI6HY7QIIFRD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTQSKI6H","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:f34e577637f0b0ff39053def5135e5aa1b9d806460d17cf6e8dbd16da673eba5","target":"graph","created_at":"2026-05-17T23:48:40Z","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":"In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the (conditional and unconditional) probability of the number of customers in the (priority) queue, orbit and system, respectively.","authors_text":"Bin Liu, Yiqiang Q. Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-03T14:18:03Z","title":"Tail Asymptotics for a Retrial Queue with Bernoulli Schedule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00984","kind":"arxiv","version":2},"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":"sha256:2c222d2cc6207f7c155ba891b5bd5c59ec5421bc90fa7d311af31188f128bb70","target":"record","created_at":"2026-05-17T23:48:40Z","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":"4705deff40c4d001ce1d3d7a6552537286e8ff9a97336ba910099e93a52712a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-03T14:18:03Z","title_canon_sha256":"199877c814a2ccc2ece9a0718d4735df045de32a26e88e195a16a23939dd2093"},"schema_version":"1.0","source":{"id":"1804.00984","kind":"arxiv","version":2}},"canonical_sha256":"ace12523c7c7e08416233c4cd1e96d5b14d0f76ab29be3d8f7f108aeb345decc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ace12523c7c7e08416233c4cd1e96d5b14d0f76ab29be3d8f7f108aeb345decc","first_computed_at":"2026-05-17T23:48:40.619652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:40.619652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aemV8a4UKiBS+ZYzatyUC4Z16EMvJOiY4APJeKFgFVLJCeB+oAR2ViUkNEXiMpsP6YoWN8d6rKkbbI/ckeCuDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:40.620273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c222d2cc6207f7c155ba891b5bd5c59ec5421bc90fa7d311af31188f128bb70","sha256:f34e577637f0b0ff39053def5135e5aa1b9d806460d17cf6e8dbd16da673eba5"],"state_sha256":"2fc374cd4ed98dd0ce5ef6be166b4dcd1e4af9db6e4a117d8cbf5b0603b02734"}