{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U4GNVIJQJNHEXSZXGRJ2GUHQQL","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":"f11521af050f76bd5bb83eef556e6cad3b7d83a5991cfb32b78da6d2a15bbee9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T22:56:48Z","title_canon_sha256":"33706eccb2f8463d81fb67d7bc44688b8e1fb3a7cfc4013c3768decafaf66aa9"},"schema_version":"1.0","source":{"id":"1303.6695","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6695","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6695v2","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6695","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"U4GNVIJQJNHE","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4GNVIJQJNHEXSZX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4GNVIJQ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:5bed400ed91c479c4c83533bb103afbc80e1e2b349553f0f66a4c5679c4b6c0a","target":"graph","created_at":"2026-05-18T01:32:43Z","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 propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties, which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of these fractional stochastic models are also pr","authors_text":"Dexter O. Cahoy, Federico Polito, Vir V. Phoha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T22:56:48Z","title":"Transient behavior of fractional queues and related processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6695","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:a0f9b473e35d2019df70d44b42a1b90a24c70d970b85386a77975acf57b29690","target":"record","created_at":"2026-05-18T01:32:43Z","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":"f11521af050f76bd5bb83eef556e6cad3b7d83a5991cfb32b78da6d2a15bbee9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T22:56:48Z","title_canon_sha256":"33706eccb2f8463d81fb67d7bc44688b8e1fb3a7cfc4013c3768decafaf66aa9"},"schema_version":"1.0","source":{"id":"1303.6695","kind":"arxiv","version":2}},"canonical_sha256":"a70cdaa1304b4e4bcb373453a350f082c298e7839fe5525a30433a4183c8a68b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a70cdaa1304b4e4bcb373453a350f082c298e7839fe5525a30433a4183c8a68b","first_computed_at":"2026-05-18T01:32:43.979929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:43.979929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0Hlqt/ZD30et6j4aeQOsofesQE4VoETBSfp0+rvYMPHODhp19+wNhzsLRCuyP2z4to4OnkJ5V3fiugwxBPoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:43.980352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6695","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0f9b473e35d2019df70d44b42a1b90a24c70d970b85386a77975acf57b29690","sha256:5bed400ed91c479c4c83533bb103afbc80e1e2b349553f0f66a4c5679c4b6c0a"],"state_sha256":"529b0998d689a81784f625512eaa632324e84b4a28da861b6e630cc00fc882eb"}