{"paper":{"title":"Delay performance in random-access grid networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.NI"],"primary_cat":"math.PR","authors_text":"Alessandro Zocca, Francesca R. Nardi, Johan S. H. van Leeuwaarden, Sem C. Borst","submitted_at":"2013-07-05T07:23:59Z","abstract_excerpt":"We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an $L\\times L$ toric grid with normalized load $\\rho$ are of the order $(\\frac{1}{1-\\rho})^L$. This superlinear delay scaling is to be contrasted with the usual linear growth of the order $\\frac{1}{1-\\rho}$ in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor im"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1532","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"}