{"paper":{"title":"Stability condition of a two-dimensional QBD process and its application to estimation of efficiency for two-queue models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Toshihisa Ozawa","submitted_at":"2018-08-20T06:25:53Z","abstract_excerpt":"In order to analyze stability of a two-queue model, we consider a two-dimensional quasi-birth-and-death process (2d-QBD process), denoted by $\\{\\boldsymbol{Y}(t)\\}=\\{((L_1(t),L_2(t)),J(t))\\}$. The two-dimensional process $\\{(L_1(t),L_2(t))\\}$ on $\\mathbb{Z}_+^2$ is called a level process, where the individual processes $\\{L_1(t)\\}$ and $\\{L_2(t)\\}$ are assumed to be skip free. The supplemental process $\\{J(t)\\}$ is called a phase process and it takes values in a finite set. The 2d-QBD process is a CTMC, in which the transition rates of the level process vary according to the state of the phase"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06319","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"}