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									                   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

     [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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