{"paper":{"title":"On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jose Blanchet, Mariana Olvera-Cravioto, Peter Glynn","submitted_at":"2010-09-28T01:50:59Z","abstract_excerpt":"Two of the most popular approximations for the distribution of the steady-state waiting time, $W_{\\infty}$, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, $\\rho$, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of $W_{\\infty}$ is roughly exponential at scale $O((1-\\rho)^{-1})$, while the heavy tailed asymptotic describes power law decay in the tail of the distribution of $W_{\\infty}$ for a fixed traffic intensity. In this paper, we ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5426","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"}