 A controlled M / G / 1 workload process with an application to perishable inventory systemsD. Perry () and W. Stadje () Mathematical Methods of Operations Research, 2006, vol. 64, issue 3, 415-428 Abstract: We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload $$a\in (0,1)$$ . The result is used to obtain the overflow distribution of this controlled workload process; we derive $$\mathbb{E}e^{-\alpha} W(T)$$ and $$\mathbb{E}[e^{{-\alpha}^{W(T)}} | W(T) \geq 1]$$ , where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period. Copyright Springer-Verlag 2006 Keywords: Controlled workload process; M / G / 1; Stationary distribution; Overflow; Perishable inventory system (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:64:y:2006:i:3:p:415-428 Ordering information: This journal article can be ordered from DOI: 10.1007/s00186-006-0094-0 Access Statistics for this article Mathematical Methods of Operations Research is currently edited by Oliver Stein More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB) |
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