{"paper":{"title":"Busy period, time of the first loss of a customer and the number of customers in $ M^{\\varkappa}|G^{\\delta}|1|B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noel Veraverbeke, Tetyana Kadankova, Victor Kadankov","submitted_at":"2011-03-21T16:07:54Z","abstract_excerpt":"A two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. More precisely, the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this instant are found. Further, we study the process reflected in its supremum. We determine the main two-boundary characteristics of the process reflected in its supremum. These results are then applied for studying the $ M^{\\varkappa}|G^{\\delta}|1|B$ system. We derive the distribution of a busy period and the numbers of custom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4064","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"}