Investigation of the Boundary Functionals of the Renewal – Reward Process with a Generalized Reflecting Barrier T. Khaniyev1, B. Gever1 and Z. Mammadova2 1 Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey 2 Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey Abstract In this study, a renewal - reward process with a generalized reflecting barrier is mathematically constructed. Moreover, the exact expressions and asymptotic expansions are obtained for the first four moments of the some boundary functionals of the process. Keywords: Renewal – reward process, Boundary functionals, Asymptotic expansion, Renewal function, Reflecting barrier. References  Aliyev, R., Okur Bekar, N., Khaniyev, T. and Unver, I., Asymptotic expansions for the moments of the boundary functionals of the renewal reward process with a discrete interference of chance, Mathematical and Computational Applications, 15, 117 – 126, 2010.  Borovkov, A.A., Asymptotic Methods in Queuing Theory, John Wiley, 1984.  Brown, M. and Solomon, H., A second – order approximation for the variance of a renewal- reward process, Stochastic Processes and Applications, 3, 301 – 314, 1975.  Khaniyev, T.A., Aliyev, R.T., Kucuk, Z. and Okur Bekar, N., On the distributions of a renewal reward process and it's additive functional, Mathematical and Computational Applications, 13(1), 41–50, 2008.
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