{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MOIYZE3OYAWQDPUROZUIINPIZA","short_pith_number":"pith:MOIYZE3O","canonical_record":{"source":{"id":"1212.0397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T14:17:26Z","cross_cats_sorted":[],"title_canon_sha256":"36d18f6619a6fe3ae1a50083312f9f6887ccaba4f436565bfd4ec2c8d24a6a77","abstract_canon_sha256":"00702e138b810541d7b650e245b5a390e82a3a5acc3815ac4d057110e30aac3a"},"schema_version":"1.0"},"canonical_sha256":"63918c936ec02d01be9176688435e8c8394cb3988b3f2cc407272ef53ea5da36","source":{"kind":"arxiv","id":"1212.0397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0397","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0397v2","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0397","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"pith_short_12","alias_value":"MOIYZE3OYAWQ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MOIYZE3OYAWQDPUR","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MOIYZE3O","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MOIYZE3OYAWQDPUROZUIINPIZA","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T14:17:26Z","cross_cats_sorted":[],"title_canon_sha256":"36d18f6619a6fe3ae1a50083312f9f6887ccaba4f436565bfd4ec2c8d24a6a77","abstract_canon_sha256":"00702e138b810541d7b650e245b5a390e82a3a5acc3815ac4d057110e30aac3a"},"schema_version":"1.0"},"canonical_sha256":"63918c936ec02d01be9176688435e8c8394cb3988b3f2cc407272ef53ea5da36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:01.320821Z","signature_b64":"a55Pp6ai1rY8uy7BIaeV9SW8KldOkatSMCnXHWOlQ3iv5Wcd8YGgu36vwcaWeKOofgkt/Eq4yBZOrx7pE6KLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63918c936ec02d01be9176688435e8c8394cb3988b3f2cc407272ef53ea5da36","last_reissued_at":"2026-05-18T03:27:01.320170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:01.320170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0397","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ych9/2TcgHqWdxR2T/Q2m+ywHTySGgHYWG35wdOPfJWEosdYBbrW9/c/IqI8MfY/j8NSQhyfRa0De2D8ucZhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:52:07.010344Z"},"content_sha256":"66bfccf2d0cd50a504d6fbd40d7f2182a88a375c1ccd4515cb1383defd724ddc","schema_version":"1.0","event_id":"sha256:66bfccf2d0cd50a504d6fbd40d7f2182a88a375c1ccd4515cb1383defd724ddc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MOIYZE3OYAWQDPUROZUIINPIZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Join the shortest queue among $k$ parallel queues: tail asymptotics of its stationary distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Masahiro Kobayashi, Masakiyo Miyazawa, Yutaka Sakuma","submitted_at":"2012-12-03T14:17:26Z","abstract_excerpt":"We are concerned with an $M/M$-type join the shortest queue ($M/M$-JSQ for short) with $k$ parallel queues for an arbitrary positive integer $k$, where the servers may be heterogeneous. We are interested in the tail asymptotic of the stationary distribution of this queueing model, provided the system is stable. We prove that this asymptotic for the minimum queue length is exactly geometric, and its decay rate is the $k$-th power of the traffic intensity of the corresponding $k$ server queues with a single waiting line. For this, we use two formulations, a quasi-birth-and-death (QBD for short) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0397","kind":"arxiv","version":2},"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":"2026-05-18T03:27:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSkbE07OINzlKcy1q60hUVobaUVnnSsEFudlB8/MGjsLydZETBo5HKjnr3KDGenHu9cnl2lGSPu0rGZI9IHYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:52:07.010694Z"},"content_sha256":"5eea946224b1d3625f23f08b5dde5cc6ef665ff947321263a36982a8de2d7ad7","schema_version":"1.0","event_id":"sha256:5eea946224b1d3625f23f08b5dde5cc6ef665ff947321263a36982a8de2d7ad7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOIYZE3OYAWQDPUROZUIINPIZA/bundle.json","state_url":"https://pith.science/pith/MOIYZE3OYAWQDPUROZUIINPIZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOIYZE3OYAWQDPUROZUIINPIZA/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":"2026-06-24T16:52:07Z","links":{"resolver":"https://pith.science/pith/MOIYZE3OYAWQDPUROZUIINPIZA","bundle":"https://pith.science/pith/MOIYZE3OYAWQDPUROZUIINPIZA/bundle.json","state":"https://pith.science/pith/MOIYZE3OYAWQDPUROZUIINPIZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOIYZE3OYAWQDPUROZUIINPIZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MOIYZE3OYAWQDPUROZUIINPIZA","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":"00702e138b810541d7b650e245b5a390e82a3a5acc3815ac4d057110e30aac3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T14:17:26Z","title_canon_sha256":"36d18f6619a6fe3ae1a50083312f9f6887ccaba4f436565bfd4ec2c8d24a6a77"},"schema_version":"1.0","source":{"id":"1212.0397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0397","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0397v2","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0397","created_at":"2026-05-18T03:27:01Z"},{"alias_kind":"pith_short_12","alias_value":"MOIYZE3OYAWQ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MOIYZE3OYAWQDPUR","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MOIYZE3O","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:5eea946224b1d3625f23f08b5dde5cc6ef665ff947321263a36982a8de2d7ad7","target":"graph","created_at":"2026-05-18T03:27:01Z","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 are concerned with an $M/M$-type join the shortest queue ($M/M$-JSQ for short) with $k$ parallel queues for an arbitrary positive integer $k$, where the servers may be heterogeneous. We are interested in the tail asymptotic of the stationary distribution of this queueing model, provided the system is stable. We prove that this asymptotic for the minimum queue length is exactly geometric, and its decay rate is the $k$-th power of the traffic intensity of the corresponding $k$ server queues with a single waiting line. For this, we use two formulations, a quasi-birth-and-death (QBD for short) ","authors_text":"Masahiro Kobayashi, Masakiyo Miyazawa, Yutaka Sakuma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T14:17:26Z","title":"Join the shortest queue among $k$ parallel queues: tail asymptotics of its stationary distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0397","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":"sha256:66bfccf2d0cd50a504d6fbd40d7f2182a88a375c1ccd4515cb1383defd724ddc","target":"record","created_at":"2026-05-18T03:27:01Z","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":"00702e138b810541d7b650e245b5a390e82a3a5acc3815ac4d057110e30aac3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-03T14:17:26Z","title_canon_sha256":"36d18f6619a6fe3ae1a50083312f9f6887ccaba4f436565bfd4ec2c8d24a6a77"},"schema_version":"1.0","source":{"id":"1212.0397","kind":"arxiv","version":2}},"canonical_sha256":"63918c936ec02d01be9176688435e8c8394cb3988b3f2cc407272ef53ea5da36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63918c936ec02d01be9176688435e8c8394cb3988b3f2cc407272ef53ea5da36","first_computed_at":"2026-05-18T03:27:01.320170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:01.320170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a55Pp6ai1rY8uy7BIaeV9SW8KldOkatSMCnXHWOlQ3iv5Wcd8YGgu36vwcaWeKOofgkt/Eq4yBZOrx7pE6KLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:01.320821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66bfccf2d0cd50a504d6fbd40d7f2182a88a375c1ccd4515cb1383defd724ddc","sha256:5eea946224b1d3625f23f08b5dde5cc6ef665ff947321263a36982a8de2d7ad7"],"state_sha256":"afb3ae38ce91426ba86e2e144bcd55142ed5e8db1c568dc70813a330d9f83047"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JYyCjuCP1o9a2CbqYZy+DOianbMnbojXCNX73NXyI9DkvP8aS/SKr9zsN5lKIFJENwrfunahxEbiYwx5xtsdBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:52:07.012555Z","bundle_sha256":"78c6f1e4c01a81e28c0e1463549fa4e21d06ca6b90ee36e382c412664e3c6b28"}}