{"paper":{"title":"Doubling Algorithms for Stationary Distributions of Fluid Queues: A Probabilistic Interpretation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Federico Poloni, Giang T. Nguyen, Nigel Bean","submitted_at":"2018-01-18T12:21:22Z","abstract_excerpt":"Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix $\\Psi$. Here, we present a probabilistic interpretation of the family of algorithms known as \\emph{doubling}, which are currently the most effective algorithms for computing the return probability matrix $\\Psi$.\n  To this end, we first revisit the links described in \\cite{ram99, soares02} between fluid queues and Quasi-Birth-Death processe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05981","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"}