{"paper":{"title":"Supermarket Queueing System in the Heavy Traffic Regime. Short Queue Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Gamarnik, Patrick Eschenfeldt","submitted_at":"2016-10-11T20:34:45Z","abstract_excerpt":"We consider a queueing system with $n$ parallel queues operating according to the so-called \"supermarket model\" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\\lambda_{n}$ Poisson arrivals and rate $1$ exponentially distributed service times, we consider this model in the heavy traffic regime, described by $\\lambda_{n}\\uparrow 1$ as $n\\to\\infty$. We give a simple expectation argument establishing that majority of queues have steady state length at least $\\log_d(1-\\lambda_{n})^{-1} - O(1)$ with probability approaching one as $n\\rightarrow\\infty$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03522","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"}