{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SBZVNDK52GV3MXSXEDZL6KMVOU","short_pith_number":"pith:SBZVNDK5","canonical_record":{"source":{"id":"1106.3858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-06-20T10:40:21Z","cross_cats_sorted":["cs.NI","math.OC"],"title_canon_sha256":"507177c9d1486a4f06e54ea50db2133ce30fdc0fce32b48fef7db4775011efb0","abstract_canon_sha256":"ed4478e4652d1e8803b3a43268465b191290ffc75631f5c51edcf8a52af1e42c"},"schema_version":"1.0"},"canonical_sha256":"9073568d5dd1abb65e5720f2bf299575121df29c2c3b37255bf1b39adb23d71b","source":{"kind":"arxiv","id":"1106.3858","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3858","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3858v1","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3858","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"SBZVNDK52GV3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBZVNDK52GV3MXSX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBZVNDK5","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SBZVNDK52GV3MXSXEDZL6KMVOU","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-06-20T10:40:21Z","cross_cats_sorted":["cs.NI","math.OC"],"title_canon_sha256":"507177c9d1486a4f06e54ea50db2133ce30fdc0fce32b48fef7db4775011efb0","abstract_canon_sha256":"ed4478e4652d1e8803b3a43268465b191290ffc75631f5c51edcf8a52af1e42c"},"schema_version":"1.0"},"canonical_sha256":"9073568d5dd1abb65e5720f2bf299575121df29c2c3b37255bf1b39adb23d71b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:43.407518Z","signature_b64":"wm8yvvkj1dc0vSDYYf/Z9ZJPyUp6XE0wcjmVePj+wLKpKY1OXrjDGtu7KubCSc7mm8wZ763wiBaJO781J4V0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9073568d5dd1abb65e5720f2bf299575121df29c2c3b37255bf1b39adb23d71b","last_reissued_at":"2026-05-18T00:58:43.406978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:43.406978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3858","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":"2026-05-18T00:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYiJ5FpTH8MU5CaCc1TKP8sonZPD83DahAQcsVcXBPJQ3jY82/dB056rSzG3D/d+bJ+/J94PzJZs7Et0EHGQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:06:57.782916Z"},"content_sha256":"29ce7623ffc3a034a535701711a0a86256960f1140f2bf11cbb8f90a4a84976d","schema_version":"1.0","event_id":"sha256:29ce7623ffc3a034a535701711a0a86256960f1140f2bf11cbb8f90a4a84976d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SBZVNDK52GV3MXSXEDZL6KMVOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Packet Dropping Mechanism for Efficient Operation of M/M/1 Queues with Selfish Users","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.OC"],"primary_cat":"cs.GT","authors_text":"Bhaskar Krishnamachari, Hua Liu, Yi Gai","submitted_at":"2011-06-20T10:40:21Z","abstract_excerpt":"We consider a fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3858","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":"2026-05-18T00:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dB/O4Rdx24iaoKJrNPrzlba6fUGElZLRcEXJCZAQ0USdrYHB64yntDhcXCDms1fUv0WMBLra3//umW6iACJmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:06:57.783663Z"},"content_sha256":"50743352396aea9b1105eed46b9d64cd3dd3f4e7b47462b9094f64750c2e6211","schema_version":"1.0","event_id":"sha256:50743352396aea9b1105eed46b9d64cd3dd3f4e7b47462b9094f64750c2e6211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/bundle.json","state_url":"https://pith.science/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/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":"2026-06-01T03:06:57Z","links":{"resolver":"https://pith.science/pith/SBZVNDK52GV3MXSXEDZL6KMVOU","bundle":"https://pith.science/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/bundle.json","state":"https://pith.science/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBZVNDK52GV3MXSXEDZL6KMVOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SBZVNDK52GV3MXSXEDZL6KMVOU","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":"ed4478e4652d1e8803b3a43268465b191290ffc75631f5c51edcf8a52af1e42c","cross_cats_sorted":["cs.NI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-06-20T10:40:21Z","title_canon_sha256":"507177c9d1486a4f06e54ea50db2133ce30fdc0fce32b48fef7db4775011efb0"},"schema_version":"1.0","source":{"id":"1106.3858","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3858","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3858v1","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3858","created_at":"2026-05-18T00:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"SBZVNDK52GV3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBZVNDK52GV3MXSX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBZVNDK5","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:50743352396aea9b1105eed46b9d64cd3dd3f4e7b47462b9094f64750c2e6211","target":"graph","created_at":"2026-05-18T00:58:43Z","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 fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. W","authors_text":"Bhaskar Krishnamachari, Hua Liu, Yi Gai","cross_cats":["cs.NI","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-06-20T10:40:21Z","title":"A Packet Dropping Mechanism for Efficient Operation of M/M/1 Queues with Selfish Users"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3858","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":"sha256:29ce7623ffc3a034a535701711a0a86256960f1140f2bf11cbb8f90a4a84976d","target":"record","created_at":"2026-05-18T00:58:43Z","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":"ed4478e4652d1e8803b3a43268465b191290ffc75631f5c51edcf8a52af1e42c","cross_cats_sorted":["cs.NI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-06-20T10:40:21Z","title_canon_sha256":"507177c9d1486a4f06e54ea50db2133ce30fdc0fce32b48fef7db4775011efb0"},"schema_version":"1.0","source":{"id":"1106.3858","kind":"arxiv","version":1}},"canonical_sha256":"9073568d5dd1abb65e5720f2bf299575121df29c2c3b37255bf1b39adb23d71b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9073568d5dd1abb65e5720f2bf299575121df29c2c3b37255bf1b39adb23d71b","first_computed_at":"2026-05-18T00:58:43.406978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:43.406978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wm8yvvkj1dc0vSDYYf/Z9ZJPyUp6XE0wcjmVePj+wLKpKY1OXrjDGtu7KubCSc7mm8wZ763wiBaJO781J4V0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:43.407518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3858","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29ce7623ffc3a034a535701711a0a86256960f1140f2bf11cbb8f90a4a84976d","sha256:50743352396aea9b1105eed46b9d64cd3dd3f4e7b47462b9094f64750c2e6211"],"state_sha256":"44e60b2358356ba0f368fd86135e4522bffe963478c55bedce4ceb3e763e68da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jucOc8K923IuPVYtfG4lpCzsm/EoHI+AyRSxcDMt39MmhKlbRHbwmwaPEA73RoM1nRvCK2kN9oWeRCEDePQdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:06:57.787087Z","bundle_sha256":"26ef23e34b80d372731b85e7b48839c5a311c98928805b1cf46323b8e05a777d"}}