dc.contributor.author Khaniyev, Tahir dc.contributor.author Gever, Basak dc.contributor.author Hanalioglu, Zulfiye dc.date.accessioned 2019-07-03T14:44:46Z dc.date.available 2019-07-03T14:44:46Z dc.date.issued 2016 dc.identifier.citation Khaniyev, 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.isbn 978-3-319-30322-2; 978-3-319-30320-8 dc.identifier.issn 2194-5357 dc.identifier.uri http://hdl.handle.net/20.500.11851/1574 dc.description 3rd International Conference on Applied Mathematics and Approximation Theory (AMAT), MAY 18-21, 2015, TOBB Econ & Technol Univ, Ankara, TURKEY en_US dc.description.abstract In 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, Turkey tr_TR dc.language.iso eng en_US dc.publisher Springer-Verlag Berlin en_US dc.relation.ispartof Advances in Intelligent Systems and Computing en_US dc.rights info:eu-repo/semantics/closedAccess dc.title Asymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrier en_US dc.type conferenceObject en_US dc.relation.journal Intelligent Mathematics II: Applied Mathematics And Approximation Theory en_US dc.contributor.department TOBB ETU, Faculty of Engineering, Department of Industrial Engineering en_US dc.contributor.department TOBB ETÜ, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü tr_TR dc.identifier.volume 441 dc.identifier.startpage 313 dc.identifier.endpage 331 dc.contributor.orcid https://orcid.org/0000-0003-1974-0140 dc.identifier.wos WOS:000377864300022 dc.identifier.scopus 2-s2.0-84961711933 dc.contributor.tobbetuauthor Khaniyev, Tahir dc.contributor.YOKid 17222 dc.identifier.doi 10.1007/978-3-319-30322-2_22 dc.contributor.ScopusAuthorID 7801652544 dc.relation.publicationcategory Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı tr_TR
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