{"paper":{"title":"Excessive Backlog Probabilities of Two Parallel Queues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ali Devin Sezer, Kamil Demirberk \\\"Unl\\\"u","submitted_at":"2018-06-02T18:49:31Z","abstract_excerpt":"Let $X$ be the constrained random walk on ${\\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and interarrival times are exponentially distributed with arrival rates $\\lambda_i$ and service rates $\\mu_i$, $i=1,2$; we assume $\\lambda_i < \\mu_i$, $i=1,2$, i.e., $X$ is assumed stable. Without loss of generality we assume $\\rho_1 =\\lambda_1/\\mu_1 \\ge \\rho_2 = \\lambda_2/\\mu_2$. Let $\\tau_n$ be the first time $X$ hits the line $\\partial A_n = \\{x \\in {\\mathbb Z}^2:x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00686","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"}