Inverse problems and inversion methods for identification of by 5w73VgGG


									                   Investigation of the Boundary Functionals
     of the Renewal – Reward Process with a Generalized Reflecting Barrier

                            T. Khaniyev1, B. Gever1 and Z. Mammadova2
    Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara,
             Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey


     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.


     [1] 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.

     [2] Borovkov, A.A., Asymptotic Methods in Queuing Theory, John Wiley, 1984.

     [3] 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.

     [4] 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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