{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:U57S44DCGHDC3TVVWBANJHYQXH","short_pith_number":"pith:U57S44DC","schema_version":"1.0","canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","source":{"kind":"arxiv","id":"1306.5002","version":1},"attestation_state":"computed","paper":{"title":"A fixed-point approximation for a routing model in equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Graham Brightwell, Malwina Luczak","submitted_at":"2013-06-20T21:03:29Z","abstract_excerpt":"We use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are $n$ nodes, each pair joined by a link of capacity $C$. For each pair of nodes, calls arrive for this pair of endpoints as a Poisson process with rate $\\lambda$. A call for endpoints $\\{u,v\\}$ is routed directly onto the link between the two nodes if there is spare capacity; otherwise $d$ two-link paths between $u$ and $v$ are considered, and the call is routed along a path with lowest maximum load, if possible. The duration of each call is an"},"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":"1306.5002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","cross_cats_sorted":[],"title_canon_sha256":"cc99da675fe5b17fbb623ccb1722d4fe017f8decf24618f1055cff01f60210e2","abstract_canon_sha256":"103a837b8067d3b45142bfe282ac048023adb4d61121532e9afe8dd640cad826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:19.996749Z","signature_b64":"NBTMUuGnfysOyGKd6ctqOSUU45gA0J+WMw1a5hXqawi+SulsCHNGYzOMfMy/BGEHIM5dlXwSjDpZ/hL7eTPZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","last_reissued_at":"2026-05-18T03:20:19.996129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:19.996129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A fixed-point approximation for a routing model in equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Graham Brightwell, Malwina Luczak","submitted_at":"2013-06-20T21:03:29Z","abstract_excerpt":"We use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are $n$ nodes, each pair joined by a link of capacity $C$. For each pair of nodes, calls arrive for this pair of endpoints as a Poisson process with rate $\\lambda$. A call for endpoints $\\{u,v\\}$ is routed directly onto the link between the two nodes if there is spare capacity; otherwise $d$ two-link paths between $u$ and $v$ are considered, and the call is routed along a path with lowest maximum load, if possible. The duration of each call is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5002","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1306.5002","created_at":"2026-05-18T03:20:19.996221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.5002v1","created_at":"2026-05-18T03:20:19.996221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5002","created_at":"2026-05-18T03:20:19.996221+00:00"},{"alias_kind":"pith_short_12","alias_value":"U57S44DCGHDC","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"U57S44DCGHDC3TVV","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"U57S44DC","created_at":"2026-05-18T12:28:02.375192+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/U57S44DCGHDC3TVVWBANJHYQXH","json":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH.json","graph_json":"https://pith.science/api/pith-number/U57S44DCGHDC3TVVWBANJHYQXH/graph.json","events_json":"https://pith.science/api/pith-number/U57S44DCGHDC3TVVWBANJHYQXH/events.json","paper":"https://pith.science/paper/U57S44DC"},"agent_actions":{"view_html":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH","download_json":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH.json","view_paper":"https://pith.science/paper/U57S44DC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.5002&json=true","fetch_graph":"https://pith.science/api/pith-number/U57S44DCGHDC3TVVWBANJHYQXH/graph.json","fetch_events":"https://pith.science/api/pith-number/U57S44DCGHDC3TVVWBANJHYQXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/action/storage_attestation","attest_author":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/action/author_attestation","sign_citation":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/action/citation_signature","submit_replication":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/action/replication_record"}},"created_at":"2026-05-18T03:20:19.996221+00:00","updated_at":"2026-05-18T03:20:19.996221+00:00"}