{"paper":{"title":"Approximation of Excessive Backlog Probabilities of Two Tandem Queues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ali Devin Sezer","submitted_at":"2018-01-15T06:25:50Z","abstract_excerpt":"Let $X$ be the constrained random walk on ${\\mathbb Z}_+^2$ taking the steps $(1,0)$, $(-1,1)$ and $(0,-1)$ with probabilities $\\lambda < (\\mu_1\\neq \\mu_2)$; in particular, $X$ is assumed stable. Let $\\tau_n$ be the first time $X$ hits $\\partial A_n = \\{x:x(1)+x(2) = n \\}$ For $x \\in {\\mathbb Z}_+^2, x(1) + x(2) < n$, the probability $p_n(x)= P_x( \\tau_n < \\tau_0)$ is a key performance measure for the queueing system represented by $X$. Let $Y$ be the constrained random walk on ${\\mathbb Z} \\times {\\mathbb Z}_+$ with increments $(-1,0)$, $(1,1)$ and $(0,-1)$. Let $\\tau$ be the first time that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04674","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"}