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dc.contributor.authorKhaniyev, Tahir
dc.contributor.authorGever, Basak
dc.contributor.authorHanalioglu, Zulfiye
dc.date.accessioned2019-07-03T14:44:46Z
dc.date.available2019-07-03T14:44:46Z
dc.date.issued2016
dc.identifier.citationKhaniyev, T., Gever, B., & Hanalioglu, Z. (2016). Asymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrier. In Intelligent Mathematics II: Applied Mathematics and Approximation Theory (pp. 313-331). Springer, Cham.en_US
dc.identifier.isbn978-3-319-30322-2; 978-3-319-30320-8
dc.identifier.issn2194-5357
dc.identifier.urihttp://hdl.handle.net/20.500.11851/1574
dc.description3rd International Conference on Applied Mathematics and Approximation Theory (AMAT), MAY 18-21, 2015, TOBB Econ & Technol Univ, Ankara, TURKEYen_US
dc.description.abstractIn this study, a renewal-reward process (X(t)) with a generalized reflecting barrier is constructed mathematically and under some weak conditions, the ergodicity of the process is proved. The explicit form of the ergodic distribution is found and after standardization, it is shown that the ergodic distribution converges to the limit distribution R(x), when lambda -> infinity, i. e., QX (lambda x) [GRAPHICS] P{X(t) <= lambda x} -> R(x) 2/m(2) [GRAPHICS] [1 - F(u)]dudv. Here, F(x) is the distribution function of the initial random variables {eta(n)}, n = 1, 2,..., which express the amount of rewards and m(2) = E(eta(2)(1)). Finally, to evaluate asymptotic rate of the weak convergence, the following inequality is obtained: vertical bar QX (lambda x) - R(x)vertical bar <= 2/lambda vertical bar pi(0)(x) - R(x)vertical bar. Here, pi(0)(x) = (1/m(1)) [GRAPHICS] (1 - F(u))du is the limit distribution of residual waiting time generated by {eta(n)}, n = 1, 2,..., and m(1) = E(eta(1)).en_US
dc.description.abstract[Khaniyev, Tahir; Gever, Basak] TOBB Univ Econ & Technol, Ankara, Turkey; [Khaniyev, Tahir] Azerbaijan Natl Acad Sci, Inst Control Syst, Baku, Azerbaijan; [Hanalioglu, Zulfiye] Karabuk Univ, Karabuk, Turkeytr_TR
dc.language.isoengen_US
dc.publisherSpringer-Verlag Berlinen_US
dc.relation.ispartofAdvances in Intelligent Systems and Computingen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.titleAsymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrieren_US
dc.typeconferenceObjecten_US
dc.relation.journalIntelligent Mathematics II: Applied Mathematics And Approximation Theoryen_US
dc.contributor.departmentTOBB ETU, Faculty of Engineering, Department of Industrial Engineeringen_US
dc.contributor.departmentTOBB ETÜ, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümütr_TR
dc.identifier.volume441
dc.identifier.startpage313
dc.identifier.endpage331
dc.contributor.orcidhttps://orcid.org/0000-0003-1974-0140
dc.identifier.wosWOS:000377864300022
dc.identifier.scopus2-s2.0-84961711933
dc.contributor.tobbetuauthorKhaniyev, Tahir
dc.contributor.YOKid17222
dc.identifier.doi10.1007/978-3-319-30322-2_22
dc.contributor.ScopusAuthorID7801652544
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıtr_TR


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