Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6321
Title: Asymptotic expansions for the moments of the boundary functionals of the renewal reward process with a discrete interference of chance
Authors: Aliyev, Rovshan
Bekar, Nurgül Okur
Khaniyev, Tahir
Ünver, Ihsan
Keywords: Renewal Reward Process
Discrete Interference of Chance
Boundary Functional
Laplace Transform
Asymptotic Expansion
Monte Carlo Method
Issue Date: 2010
Publisher: Mdpi
Abstract: In this study, two boundary functionals N-1 and tau(1) of the renewal reward process with a discrete interference of chance ( X(t)) are investigated. A relation between the moment generating function (Psi(N)(z)) of the boundary functional N-1 and the Laplace transform (Phi(tau)(mu)) of the boundary functional tau(1) is obtained. Using this relation, the exact formulas for the first four moments of the boundary functional tau(1) are expressed by means of the first four moments of the boundary functional N-1. Moreover, the asymptotic expansions for the first four moments of these boundary functionals are established when the random variables {zeta(n)}, n >= 0, which describe a discrete interference of chance, have an exponential distribution with parameter lambda > 0. Finally, the accuracy of the approximation formulas for the moments (EN1k) of the boundary functional N-1 are tested by Monte Carlo simulation method.
URI: https://hdl.handle.net/20.500.11851/6321
ISSN: 1300-686X
2297-8747
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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