{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FFA6O52CIVTXR5ZU6OR2GO5RL3","short_pith_number":"pith:FFA6O52C","schema_version":"1.0","canonical_sha256":"2941e77742456778f734f3a3a33bb15ef0bd451b8297ecd7ceba0d9baab7a4c6","source":{"kind":"arxiv","id":"1707.05143","version":3},"attestation_state":"computed","paper":{"title":"Queues Driven by Hawkes Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Daw, Jamol Pender","submitted_at":"2017-07-17T13:29:16Z","abstract_excerpt":"Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through self-excitation of the arrival process. In this paper, we analyze an infinite server queueing system in which the arrivals are driven by the self-exciting Hawkes process and where service follows a phase-type distribution or is deterministic. In the phase-type setting, we derive differential equations for the moments and a partial differential equation for the moment generating function; we also derive exact expressions for the tran"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.05143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-17T13:29:16Z","cross_cats_sorted":[],"title_canon_sha256":"5446949f4370ef94ea631ae742dea7c895b364db41657f5edc4ec8b9bf467380","abstract_canon_sha256":"5490f47ff824e6bcf4548ff58717eb8f85a20e9e9c9b869bf4e223da6ec59a24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:23.689771Z","signature_b64":"oRUqH67dXVPK8luUPhl+cHdnxVReaPEJGpMJOBbdGBYK2Zvt9DFcxS2GWmw14KTvF+IHAvxzHbkWnmzqMEmzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2941e77742456778f734f3a3a33bb15ef0bd451b8297ecd7ceba0d9baab7a4c6","last_reissued_at":"2026-05-18T00:16:23.689278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:23.689278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Queues Driven by Hawkes Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Daw, Jamol Pender","submitted_at":"2017-07-17T13:29:16Z","abstract_excerpt":"Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through self-excitation of the arrival process. In this paper, we analyze an infinite server queueing system in which the arrivals are driven by the self-exciting Hawkes process and where service follows a phase-type distribution or is deterministic. In the phase-type setting, we derive differential equations for the moments and a partial differential equation for the moment generating function; we also derive exact expressions for the tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05143","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.05143","created_at":"2026-05-18T00:16:23.689355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05143v3","created_at":"2026-05-18T00:16:23.689355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05143","created_at":"2026-05-18T00:16:23.689355+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFA6O52CIVTX","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFA6O52CIVTXR5ZU","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFA6O52C","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3","json":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3.json","graph_json":"https://pith.science/api/pith-number/FFA6O52CIVTXR5ZU6OR2GO5RL3/graph.json","events_json":"https://pith.science/api/pith-number/FFA6O52CIVTXR5ZU6OR2GO5RL3/events.json","paper":"https://pith.science/paper/FFA6O52C"},"agent_actions":{"view_html":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3","download_json":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3.json","view_paper":"https://pith.science/paper/FFA6O52C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05143&json=true","fetch_graph":"https://pith.science/api/pith-number/FFA6O52CIVTXR5ZU6OR2GO5RL3/graph.json","fetch_events":"https://pith.science/api/pith-number/FFA6O52CIVTXR5ZU6OR2GO5RL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3/action/storage_attestation","attest_author":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3/action/author_attestation","sign_citation":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3/action/citation_signature","submit_replication":"https://pith.science/pith/FFA6O52CIVTXR5ZU6OR2GO5RL3/action/replication_record"}},"created_at":"2026-05-18T00:16:23.689355+00:00","updated_at":"2026-05-18T00:16:23.689355+00:00"}