{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6QANLGUSVGM6LE75ZOVNZFGI5Y","short_pith_number":"pith:6QANLGUS","canonical_record":{"source":{"id":"1507.05298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-19T15:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"fb2701c083004854017011faa21724594da22b3366ee8f242d5bfeb51d8baf64","abstract_canon_sha256":"96bd4ac374beb1dec5054639a7293a078fdae35b542c1bf3ac0d71e2c8389109"},"schema_version":"1.0"},"canonical_sha256":"f400d59a92a999e593fdcbaadc94c8ee0572b3169a1f5caaa323c1efdfa7b5d2","source":{"kind":"arxiv","id":"1507.05298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05298","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05298v1","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05298","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"6QANLGUSVGM6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6QANLGUSVGM6LE75","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6QANLGUS","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6QANLGUSVGM6LE75ZOVNZFGI5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-19T15:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"fb2701c083004854017011faa21724594da22b3366ee8f242d5bfeb51d8baf64","abstract_canon_sha256":"96bd4ac374beb1dec5054639a7293a078fdae35b542c1bf3ac0d71e2c8389109"},"schema_version":"1.0"},"canonical_sha256":"f400d59a92a999e593fdcbaadc94c8ee0572b3169a1f5caaa323c1efdfa7b5d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:37.277636Z","signature_b64":"zYzFCNovSLB473rBMe3K0fRlNZ7yGG/bB3zTgvukvUrNO2XZLZ9Y4v/mnl9K/eoXuJqCNcTvzvsTqH53ytE8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f400d59a92a999e593fdcbaadc94c8ee0572b3169a1f5caaa323c1efdfa7b5d2","last_reissued_at":"2026-05-18T01:36:37.276889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:37.276889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05298","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dt+f7nCoNo0yDWqYvS2wZFdk6lb727WU14K7aBroqDQvp+6nIK/bJDJ7rJy3Mxr7RMtAVfc9jJhvlPZhMU9eDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T01:20:16.699755Z"},"content_sha256":"0b6af06f23458cff79734f51f932c54a3ba78f8dee316ff77d455506824a4d7e","schema_version":"1.0","event_id":"sha256:0b6af06f23458cff79734f51f932c54a3ba78f8dee316ff77d455506824a4d7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6QANLGUSVGM6LE75ZOVNZFGI5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level product form QSF processes and an analysis of queues with Coxian inter-arrival distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dwi Ertiningsih, Floske M. Spieksma, Laurens C. Smit, Michael N. Katehakis","submitted_at":"2015-07-19T15:16:27Z","abstract_excerpt":"In this paper we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the ${\\it Cox(k)}/M^Y/1$-queue, that can be modelled as a QSF process on a two-dimensional state space. In addition we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05298","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O/yo5XBaymNa8VAclLdxfuiw0JkuoZgai6j5Hw4Op75OLymer3FtHcmLHhS1NQ3oVGEYFage405MRho/3lg7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T01:20:16.700101Z"},"content_sha256":"f16f642de8ad193a1669688c4bc938aeeeccff8b5713906021cc84d04320ff1d","schema_version":"1.0","event_id":"sha256:f16f642de8ad193a1669688c4bc938aeeeccff8b5713906021cc84d04320ff1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/bundle.json","state_url":"https://pith.science/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T01:20:16Z","links":{"resolver":"https://pith.science/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y","bundle":"https://pith.science/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/bundle.json","state":"https://pith.science/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QANLGUSVGM6LE75ZOVNZFGI5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6QANLGUSVGM6LE75ZOVNZFGI5Y","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":"96bd4ac374beb1dec5054639a7293a078fdae35b542c1bf3ac0d71e2c8389109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-19T15:16:27Z","title_canon_sha256":"fb2701c083004854017011faa21724594da22b3366ee8f242d5bfeb51d8baf64"},"schema_version":"1.0","source":{"id":"1507.05298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05298","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05298v1","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05298","created_at":"2026-05-18T01:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"6QANLGUSVGM6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6QANLGUSVGM6LE75","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6QANLGUS","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:f16f642de8ad193a1669688c4bc938aeeeccff8b5713906021cc84d04320ff1d","target":"graph","created_at":"2026-05-18T01:36:37Z","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":"In this paper we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the ${\\it Cox(k)}/M^Y/1$-queue, that can be modelled as a QSF process on a two-dimensional state space. In addition we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queu","authors_text":"Dwi Ertiningsih, Floske M. Spieksma, Laurens C. Smit, Michael N. Katehakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-19T15:16:27Z","title":"Level product form QSF processes and an analysis of queues with Coxian inter-arrival distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05298","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":"sha256:0b6af06f23458cff79734f51f932c54a3ba78f8dee316ff77d455506824a4d7e","target":"record","created_at":"2026-05-18T01:36:37Z","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":"96bd4ac374beb1dec5054639a7293a078fdae35b542c1bf3ac0d71e2c8389109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-19T15:16:27Z","title_canon_sha256":"fb2701c083004854017011faa21724594da22b3366ee8f242d5bfeb51d8baf64"},"schema_version":"1.0","source":{"id":"1507.05298","kind":"arxiv","version":1}},"canonical_sha256":"f400d59a92a999e593fdcbaadc94c8ee0572b3169a1f5caaa323c1efdfa7b5d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f400d59a92a999e593fdcbaadc94c8ee0572b3169a1f5caaa323c1efdfa7b5d2","first_computed_at":"2026-05-18T01:36:37.276889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:37.276889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zYzFCNovSLB473rBMe3K0fRlNZ7yGG/bB3zTgvukvUrNO2XZLZ9Y4v/mnl9K/eoXuJqCNcTvzvsTqH53ytE8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:37.277636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b6af06f23458cff79734f51f932c54a3ba78f8dee316ff77d455506824a4d7e","sha256:f16f642de8ad193a1669688c4bc938aeeeccff8b5713906021cc84d04320ff1d"],"state_sha256":"18953ab3cb1fe86ffb3e9ed04a11e1aa4dab324bf453ebdd81a9d09c0bdd688e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxTRVusBBHxocNq23b4sKN2NhmznWbIOocEg6Iwtdta7JtqLT7inBlRXazln2hqOzazxkqMwaqNFz8JK8E96BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T01:20:16.702108Z","bundle_sha256":"169b83da4e0f2f3d5a7ec88768222f860e9a4768d899fd8b8a78316c8ecc6daa"}}