{"paper":{"title":"A L\\'{e}vy input model with additional state-dependent services","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Vlasiou, Zbigniew Palmowski","submitted_at":"2009-02-03T11:56:50Z","abstract_excerpt":"We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\\{e_q^{(i)}\\}_{i=1,2,...}$ according to a spectrally positive L\\'{e}vy process $Y(t)$ which is reflected at 0. When the exponential clock $e_q^{(i)}$ ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to $F_i(Y(e_q^{(i)}))$ at epoch $e^{(1)}_q+...+e^{(i)}_q$ for some random nonnegative i.i.d. functionals $F_i$. In particular, we focus on the case when $F_i(y)=(B_i-y)^+$, where $\\{B_i\\}_{i=1,2,...}$ are i.i.d. nonnegative random variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0485","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"}