{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2QG4ROBEOZ74ZXEP5DU6JPEVIE","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":"08e2d1da1a98459934c1cca4b2333ef68c335c219019621e4e9f68cad77eadf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T08:24:00Z","title_canon_sha256":"f1b180ca377fa377828c9a8cff47b2dee39f9be09d72c10a8fd1bb93f5e66a88"},"schema_version":"1.0","source":{"id":"1607.08722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08722","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08722v2","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08722","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"2QG4ROBEOZ74","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2QG4ROBEOZ74ZXEP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2QG4ROBE","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:d03033083146b9d6986dc02538eed1fe7663e45e43e54f6a6f4ee590a08843b7","target":"graph","created_at":"2026-05-18T00:48:37Z","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 analyze the time-dependent behavior of an $M/M/c$ priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least $c$ high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most $c - 1$ high-priority customers. We then show how to compute the remaining Laplace transforms recursive","authors_text":"Brian Fralix, Jori Selen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T08:24:00Z","title":"Time-dependent analysis of an $M/M/c$ preemptive priority system with two priority classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08722","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":"sha256:332a57578193b54b85d3f35014dd1a4b000c9ff94c4f8c73ad3865780aba33a0","target":"record","created_at":"2026-05-18T00:48:37Z","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":"08e2d1da1a98459934c1cca4b2333ef68c335c219019621e4e9f68cad77eadf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-29T08:24:00Z","title_canon_sha256":"f1b180ca377fa377828c9a8cff47b2dee39f9be09d72c10a8fd1bb93f5e66a88"},"schema_version":"1.0","source":{"id":"1607.08722","kind":"arxiv","version":2}},"canonical_sha256":"d40dc8b824767fccdc8fe8e9e4bc9541220b36cdc940112441df90895e90eaf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d40dc8b824767fccdc8fe8e9e4bc9541220b36cdc940112441df90895e90eaf5","first_computed_at":"2026-05-18T00:48:37.195508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:37.195508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wwd41Zk6c1OpT5hiF6dvsYljAG7HkJ5tzXMOUvU5Zbcp9fnyO+kMZB49Abe255KHGjUYyVF5mqXnMnAYoVETBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:37.196477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:332a57578193b54b85d3f35014dd1a4b000c9ff94c4f8c73ad3865780aba33a0","sha256:d03033083146b9d6986dc02538eed1fe7663e45e43e54f6a6f4ee590a08843b7"],"state_sha256":"73b7282398109112b5b719658e3d184d196b720e79acdc1d89daf936505ee2bf"}