{"paper":{"title":"On the optimal tradeoff of average service cost rate, average utility rate, and average delay for the state dependent M/M/1 queue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.OC"],"primary_cat":"cs.PF","authors_text":"Utpal Mukherji, Vineeth B. S.","submitted_at":"2013-11-03T16:07:43Z","abstract_excerpt":"The optimal tradeoff between average service cost rate, average utility rate, and average delay is addressed for a state dependent M/M/1 queueing model, with controllable queue length dependent service rates and arrival rates. For a model with a constant arrival rate $\\lambda$ for all queue lengths, we obtain an asymptotic characterization of the minimum average delay, when the average service cost rate is a small positive quantity, $V$, more than the minimum average service cost rate required for queue stability. We show that depending on the value of the arrival rate $\\lambda$, the assumed s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0486","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"}