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Asymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrier

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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 Uluslararası yayın tr_TR


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