{"paper":{"title":"The correlation function of a queue with Levy and Markov additive input","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Agata Cichocka, Michel Mandjes, Wouter Berkelmans","submitted_at":"2019-06-06T18:38:18Z","abstract_excerpt":"Let $(Q_t)$ be a stationary workload process, and $r(t)$ the correlation coefficient of $Q_0$ and $Q_t$. In a series of previous papers (i) the transform of $r(\\cdot)$ has been derived for the case that the driving process is spectrally-positive (sp) or spectrally-negative (sn) Levy, (ii) it has been shown that for sp-Levy and sn-Levy input $r(\\cdot)$ is positive, decreasing, and convex, (iii) in case the driving Levy process is light-tailed (a condition that is automatically fulfilled in the sn case), the decay of the decay rate agrees with that of the tail of the busy period distribution. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02766","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"}