{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PBDCBMQFDIW7NN3X6KQPHWLECX","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":"a5e4b14e44cec903de7c7981282b318089bca342d20beb67c6c1d059cebf224b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-17T08:08:37Z","title_canon_sha256":"801df49c30aa0a4a5728fb0373384f264f14022a2cf213c6d2a7aa30e7f87358"},"schema_version":"1.0","source":{"id":"1310.4608","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4608","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4608v3","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4608","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"PBDCBMQFDIW7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PBDCBMQFDIW7NN3X","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PBDCBMQF","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:fa06b29e5de836933ce9e03c3e00660575e7117f23f5b5d43c8cd4511586083e","target":"graph","created_at":"2026-05-18T02:48:17Z","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":"The main contribution of this paper is to prove the subexponential tail equivalence of the stationary queue length distributions in the BMAP/GI/1 queues with and without retrials. We first present a stochastic-decomposition-like result of the stationary queue length in the BMAP/GI/1 retrial queue, which is an extension of the stochastic decomposition of the stationary queue length in the M${}^X$/GI/1 retrial queue. The stochastic-decomposition-like result shows that the stationary queue length distribution in the BMAP/GI/1 retrial queue is decomposed into two parts: the stationary conditional ","authors_text":"Hiroyuki Masuyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-17T08:08:37Z","title":"Subexponential tail equivalence of the queue length distributions of BMAP/GI/1 queues with and without retrials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4608","kind":"arxiv","version":3},"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":"sha256:68467cd6d01aa74811cee33a9541d2b82dbe760e693d55e63c92ad3f543f76a9","target":"record","created_at":"2026-05-18T02:48:17Z","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":"a5e4b14e44cec903de7c7981282b318089bca342d20beb67c6c1d059cebf224b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-17T08:08:37Z","title_canon_sha256":"801df49c30aa0a4a5728fb0373384f264f14022a2cf213c6d2a7aa30e7f87358"},"schema_version":"1.0","source":{"id":"1310.4608","kind":"arxiv","version":3}},"canonical_sha256":"784620b2051a2df6b777f2a0f3d96415dfc03059f0a3e0eab225fb6bca2abb1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"784620b2051a2df6b777f2a0f3d96415dfc03059f0a3e0eab225fb6bca2abb1e","first_computed_at":"2026-05-18T02:48:17.558794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.558794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L2pzRz58uVG9qiwqkqITlXVmJP/++wy3jGkXLIQsWX4umvIBISWU6DiiuyKEuXz6riTbRtTZlwRzDaDAHDmeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.559260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4608","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68467cd6d01aa74811cee33a9541d2b82dbe760e693d55e63c92ad3f543f76a9","sha256:fa06b29e5de836933ce9e03c3e00660575e7117f23f5b5d43c8cd4511586083e"],"state_sha256":"ee385f70c79190a0aeb0bada528eef329abf737e7dbab0987db1618caf71f7d9"}