On the Boundary Functional of the Random Walk With Two Barriers Related To Optimal Capacity of the Buffer Stock

Abstract

In this study, a boundary functional (N) of the semi-Markovian random walk (X (t)) with two special barriers is considered. The boundary functional N is defined as the first time when the random walk exits from the interval (a). In this study, the boundary functional N has been investigated under the assumption that the jumps of the random walk are expressed by bilateral exponential distributed random variables. There are significant implementations of the boundary functional N in the stock control theory. Especially, it is important to investigate numerical characteristics of the boundary functional N for the finding optimal capacity of buffer stock located between two machines which are working at the same speed. For this reason, the exact expressions for the first three moments of the boundary functional N are obtained by using basic identity for random walk (Feller (1971)). Next, the exact and approximation expressions for the expected value, variance, standard deviation, variation and skewness coefficients of the boundary functional N are derived.

[Hanalioglu, Z.] Karabuk Univ, Dept Actuary & Risk Management, Karabuk, Turkey; [Gever, B.] STM Def Technol & Trade Inc, Artificial Engn & Data Fus, Ankara, Turkey; [Poladova, A.; Khaniyev, T.] TOBB Univ Econ & Technol, Dept Ind Engn, Ankara, Turkey