{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:57WTC53J24M7SQR4PEXFYXHXC5","short_pith_number":"pith:57WTC53J","canonical_record":{"source":{"id":"1302.3144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T15:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"3f65197a352180ce9f6e9f89a813a014ff11bda944a6a02e39533d5792185ac7","abstract_canon_sha256":"cb0206fe1c29c89e2f339283e4c3eaa2d9c577dcc6fd02eb14689d76c0eac0b8"},"schema_version":"1.0"},"canonical_sha256":"efed317769d719f9423c792e5c5cf7174a4b9721e790e7c3a3b0b80fce5a5208","source":{"kind":"arxiv","id":"1302.3144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3144","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3144v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3144","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"57WTC53J24M7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57WTC53J24M7SQR4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57WTC53J","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:57WTC53J24M7SQR4PEXFYXHXC5","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T15:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"3f65197a352180ce9f6e9f89a813a014ff11bda944a6a02e39533d5792185ac7","abstract_canon_sha256":"cb0206fe1c29c89e2f339283e4c3eaa2d9c577dcc6fd02eb14689d76c0eac0b8"},"schema_version":"1.0"},"canonical_sha256":"efed317769d719f9423c792e5c5cf7174a4b9721e790e7c3a3b0b80fce5a5208","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:48.575635Z","signature_b64":"dfzfnl3f4RqJSs5gsG1Griimn0TMYgCQns4PzZsx/NOH7OAePqGxW4mpgYarbGps9QrnTxhjfNznEoHkLrEzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efed317769d719f9423c792e5c5cf7174a4b9721e790e7c3a3b0b80fce5a5208","last_reissued_at":"2026-05-18T03:33:48.574808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:48.574808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3144","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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zw5OROsgVdGdCi0pso92orde3kDR366hQ/eskX+yIdAg0yYGqhHqeSJVZiqZAZg7OffrrQxnEj8ovUOMuULsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:12:33.063923Z"},"content_sha256":"276f25d594b0e22d38f6f48dbb60fe8466777f731a97100df374f0586719729e","schema_version":"1.0","event_id":"sha256:276f25d594b0e22d38f6f48dbb60fe8466777f731a97100df374f0586719729e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:57WTC53J24M7SQR4PEXFYXHXC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Queues with random back-offs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johan S.H. van Leeuwaarden, Niek Bouman, Onno J. Boxma, Sem C. Borst","submitted_at":"2013-02-13T15:48:48Z","abstract_excerpt":"We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3144","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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ADfBZ6CsvDndmWHSFsVNL9c8pW0NK1bO0mtVNuSHTGMc3dxJI0jMNOMI2Kj/aK0U5zUN7uks0Ak93RKtzApBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:12:33.064640Z"},"content_sha256":"dc83ef350e2739a37a2ac646ad440d137857af06785f99e14f19359543467742","schema_version":"1.0","event_id":"sha256:dc83ef350e2739a37a2ac646ad440d137857af06785f99e14f19359543467742"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57WTC53J24M7SQR4PEXFYXHXC5/bundle.json","state_url":"https://pith.science/pith/57WTC53J24M7SQR4PEXFYXHXC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57WTC53J24M7SQR4PEXFYXHXC5/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":"2026-05-28T21:12:33Z","links":{"resolver":"https://pith.science/pith/57WTC53J24M7SQR4PEXFYXHXC5","bundle":"https://pith.science/pith/57WTC53J24M7SQR4PEXFYXHXC5/bundle.json","state":"https://pith.science/pith/57WTC53J24M7SQR4PEXFYXHXC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57WTC53J24M7SQR4PEXFYXHXC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:57WTC53J24M7SQR4PEXFYXHXC5","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":"cb0206fe1c29c89e2f339283e4c3eaa2d9c577dcc6fd02eb14689d76c0eac0b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T15:48:48Z","title_canon_sha256":"3f65197a352180ce9f6e9f89a813a014ff11bda944a6a02e39533d5792185ac7"},"schema_version":"1.0","source":{"id":"1302.3144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3144","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3144v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3144","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"57WTC53J24M7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"57WTC53J24M7SQR4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"57WTC53J","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:dc83ef350e2739a37a2ac646ad440d137857af06785f99e14f19359543467742","target":"graph","created_at":"2026-05-18T03:33:48Z","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 broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In p","authors_text":"Johan S.H. van Leeuwaarden, Niek Bouman, Onno J. Boxma, Sem C. Borst","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T15:48:48Z","title":"Queues with random back-offs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3144","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":"sha256:276f25d594b0e22d38f6f48dbb60fe8466777f731a97100df374f0586719729e","target":"record","created_at":"2026-05-18T03:33:48Z","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":"cb0206fe1c29c89e2f339283e4c3eaa2d9c577dcc6fd02eb14689d76c0eac0b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T15:48:48Z","title_canon_sha256":"3f65197a352180ce9f6e9f89a813a014ff11bda944a6a02e39533d5792185ac7"},"schema_version":"1.0","source":{"id":"1302.3144","kind":"arxiv","version":1}},"canonical_sha256":"efed317769d719f9423c792e5c5cf7174a4b9721e790e7c3a3b0b80fce5a5208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efed317769d719f9423c792e5c5cf7174a4b9721e790e7c3a3b0b80fce5a5208","first_computed_at":"2026-05-18T03:33:48.574808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:48.574808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dfzfnl3f4RqJSs5gsG1Griimn0TMYgCQns4PzZsx/NOH7OAePqGxW4mpgYarbGps9QrnTxhjfNznEoHkLrEzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:48.575635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:276f25d594b0e22d38f6f48dbb60fe8466777f731a97100df374f0586719729e","sha256:dc83ef350e2739a37a2ac646ad440d137857af06785f99e14f19359543467742"],"state_sha256":"907e8535b0345f72005f1dfe05ef5e0bdcba0367fd0a6fd1f13f448cea902d0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YLfqeanQZTCbbgN5EZ4xG5fv0b0HZipg+0Q3mHepTL2+5/xaDVCSt7hJyOQdrRz7CH4qpFb9ZlZ5+Y/vRIaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:12:33.068449Z","bundle_sha256":"552402e8a05ae1cb6dd78b9fb8e96b5d5193ec630084e193e33621b0e38f6345"}}