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Abstract: In this study, a buffer stock between two machines which are working at the same
speed, is considered. It is assumed that the stock level between two machines alters in the
interval 0 , 2α. In the case that only the first machine is broken, the stock level can decrease
to zero if repairing time of the first machine is extended. This causes the second machine is
required to be halted. After fixing the first machine, the system begins to work again. If the
second machine is broken and the first machine is working, then the process proceeds until the
stock level reaches the maximum level 2α and then the first machine will be halt compulsory.
In order to re-work the system, the repairing of the second machine must be completed. Under
these assumptions, the buffer stock level will be stochastically fluctuated in the interval 0 , 2α. Thus, the buffer stock between two machines can be expressed by a stochastic process Y t and
it is observed that this process is a random walk with two barriers. Some problems of queuing
theory, stock control, reliability, insurance models and risk management can be expressed by
random walk and its modifications. In literature, there are several considerable studies (e.g.,
Aliyev and Khaniyev, Feller, Janseen and Leeuwarden, etc.). In this study, the stationary
characteristics of the random walk process Y t which represent the buffer stock level, are
investigated. Especially, for all moments of the ergodic distribution of the process Y t, the exact
expressions are obtained under the assumption that the random walk Y t generated by bilateral
exponential distributed summands. Moreover, the exact and approximate expressions for
variance, standard deviation, coefficient of variation, skewness and kurtosis of the process, are
obtained. It is also observed that the ergodic distribution of the standardized stochastic process
W t = Y t / a weakly converges to a triangular distribution in the interval 0, 2.
International Data Science & Engineering Symposium
IDSES
Zülfiye HANALİOGLU
Tahir HANALİOGLU