{"paper":{"title":"Necessary condition for null controllability in many-server heavy traffic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gennady Shaikhet","submitted_at":"2015-01-26T07:56:22Z","abstract_excerpt":"Throughput sub-optimality (TSO), introduced in Atar and Shaikhet [Ann. Appl. Probab. 19 (2009) 521-555] for static fluid models of parallel queueing networks, corresponds to the existence of a resource allocation, under which the total service rate becomes greater than the total arrival rate. As shown in Atar, Mandelbaum and Shaikhet [Ann. Appl. Probab. 16 (2006) 1764-1804] and Atar and Shaikhet (2009), in the many server Halfin-Whitt regime, TSO implies null controllability (NC), the existence of a routing policy under which, for every finite $T$, the measure of the set of times prior to $T$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06277","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"}