{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XWU5JKFQ42KMQ773OJ4SS7AY26","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":"1b1d03e40fedc6b9ce47a461dde62451d77337777923bf57547159d33fe793e8","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2016-12-07T22:14:56Z","title_canon_sha256":"7e9acb846c81971886a7d93498198e5ef911652361c56248fe91219e5e166594"},"schema_version":"1.0","source":{"id":"1701.01328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01328","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01328v1","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01328","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"XWU5JKFQ42KM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XWU5JKFQ42KMQ773","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XWU5JKFQ","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:0afce703ab9dfdc217344826b94a98e6a30e4c267f11579d171ec788c1ec37e4","target":"graph","created_at":"2026-05-18T00:53:19Z","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 consider a Markovian many server queueing system in which customers are preemptively scheduled according to exogenously assigned priority levels. The priority levels are randomly assigned from a continuous probability measure rather than a discrete one and hence, the queue is modeled by an infinite dimensional stochastic process. We analyze the equilibrium behavior of the system and provide several results. We derive the Radon-Nikodym derivative (with respect to Lebesgue measure) of the measure that describes the average distribution of customer priority levels in the system; we provide a f","authors_text":"Neal Master, Nicholas Bambos, Zhengyuan Zhou","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2016-12-07T22:14:56Z","title":"An Infinite Dimensional Model for a Many Server Priority Queue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01328","kind":"arxiv","version":1},"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:fc537d78c46eacbcb09eb8e60ceb667af71d2b8b85af4489616033ee54366419","target":"record","created_at":"2026-05-18T00:53:19Z","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":"1b1d03e40fedc6b9ce47a461dde62451d77337777923bf57547159d33fe793e8","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PF","submitted_at":"2016-12-07T22:14:56Z","title_canon_sha256":"7e9acb846c81971886a7d93498198e5ef911652361c56248fe91219e5e166594"},"schema_version":"1.0","source":{"id":"1701.01328","kind":"arxiv","version":1}},"canonical_sha256":"bda9d4a8b0e694c87ffb7279297c18d783ab1fcf36eb18d9f68576780d7fc47c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bda9d4a8b0e694c87ffb7279297c18d783ab1fcf36eb18d9f68576780d7fc47c","first_computed_at":"2026-05-18T00:53:19.888391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:19.888391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bak9wwnwvX1ZiVibWvL3ngHua9b/OJHackoIJFRW97FLaoxkpQ0AIpGcdF1FcA4ESDQvVTphXQ5TiaEMzWr5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:19.888913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc537d78c46eacbcb09eb8e60ceb667af71d2b8b85af4489616033ee54366419","sha256:0afce703ab9dfdc217344826b94a98e6a30e4c267f11579d171ec788c1ec37e4"],"state_sha256":"786c7ecb949a178b6869aaad93e2f48966b48966f66c2d3f868e9050b22c7d03"}