{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QHIFVH4B33T7IUXSCEVHLYOPBL","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":"2fadcc3943c3d729e499576bce51fcd7aa508b48dda28c72f5565db1c26070a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-18T19:35:02Z","title_canon_sha256":"825815bb6a360b242c48a0ed04d8823455092c937861ba17f11373943aea2584"},"schema_version":"1.0","source":{"id":"1807.07115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07115","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07115v2","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07115","created_at":"2026-05-17T23:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"QHIFVH4B33T7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHIFVH4B33T7IUXS","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHIFVH4B","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:72cce92442bfc271bb61f4c03104857f812a906f1bc76af7c218bcf50fa45684","target":"graph","created_at":"2026-05-17T23:57:50Z","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":"A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by a continuous drift-diffusion process a Smoluchowski equation on the half space is derived approximating the forward Kolmogorov equations. The approximate model is analyzed and validated, showing excellent agreement for the probabilities of all queue lengths and for all queuing utilizations, including ones that are very small and some that are significantly ","authors_text":"Dieter Armbruster, Simone G\\\"ottlich, Stephan Knapp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-18T19:35:02Z","title":"Continuous approximation of $M_t/M_t/1$ distributions with application to production"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07115","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":"sha256:68620ff3d5fe86f13c8fb07acc2a9622031c1ab5273a4ed68cd32f7269c2536d","target":"record","created_at":"2026-05-17T23:57:50Z","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":"2fadcc3943c3d729e499576bce51fcd7aa508b48dda28c72f5565db1c26070a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-18T19:35:02Z","title_canon_sha256":"825815bb6a360b242c48a0ed04d8823455092c937861ba17f11373943aea2584"},"schema_version":"1.0","source":{"id":"1807.07115","kind":"arxiv","version":2}},"canonical_sha256":"81d05a9f81dee7f452f2112a75e1cf0aeb016d25aee7186f6fdb31574254ef59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81d05a9f81dee7f452f2112a75e1cf0aeb016d25aee7186f6fdb31574254ef59","first_computed_at":"2026-05-17T23:57:50.495886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:50.495886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LPbCRKZQfuwl1vxofDnhmiIe8FYwa9E1RgDOYYl508SSeezY7akGjPyxkPS+9dxTxKSHr4XHq1ErO2xPvQGSCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:50.496546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68620ff3d5fe86f13c8fb07acc2a9622031c1ab5273a4ed68cd32f7269c2536d","sha256:72cce92442bfc271bb61f4c03104857f812a906f1bc76af7c218bcf50fa45684"],"state_sha256":"53e7c909735b393b6fdc8e7eef3ac639e09ecf2a6346bc2d7aa079c8914c22b0"}