{"paper":{"title":"Useful stochastic bounds in time-varying queues with service and patience times having general joint distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Royi Jacobovic, Shreehari Anand Bodas","submitted_at":"2024-06-18T16:06:18Z","abstract_excerpt":"Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\\lambda:[0,\\infty)\\rightarrow[0,\\lambda_h ]$ for some $\\lambda_h>0$. For each $i\\in\\mathbb{N}$, let $S_i$ (resp., $Y_i$) be the service (resp., patience) time of the $i$'th customer and assume that $(S_1,Y_1),(S_2,Y_2),\\ldots$ is an iid sequence of bivariate random vectors with non-negative coordinates. A customer joins if and only if his patience time is not less than his prospective waiting time (i.e., the left-limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12745","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.12745/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}