{"paper":{"title":"Gaussian queues in light and heavy traffic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosinski, Krzysztof Debicki, Michel Mandjes","submitted_at":"2011-04-01T13:30:06Z","abstract_excerpt":"In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\\equiv\\{X(t):t\\in\\mathbb R\\}$ with stationary increments and variance function $\\sigma^2_X(\\cdot)$, equipped with a deterministic drift $c>0$, reflected at 0: \\[Q_X^{(c)}(t)=\\sup_{-\\infty<s\\le t}(X(t)-X(s)-c(t-s)).\\] We study the resulting stationary workload process $Q^{(c)}_X\\equiv\\{Q_X^{(c)}(t):t\\ge0\\}$ in the limiting regimes $c\\to 0$ (heavy traffic) and $c\\to\\infty$ (light traffic). The primary contribution is that we show for b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0167","kind":"arxiv","version":2},"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"}