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dc.contributor.authorKhaniyev, Tahir
dc.contributor.authorGever, Basak
dc.contributor.authorHanalioglu, Zulfiye
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.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.publisherSpringer-Verlag Berlinen_US
dc.relation.ispartofAdvances in Intelligent Systems and Computingen_US
dc.titleAsymptotic Rate for Weak Convergence of the Distribution of Renewal-Reward Process with a Generalized Reflecting Barrieren_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.contributor.tobbetuauthorKhaniyev, Tahir
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıtr_TR

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