A stochastic model for the circulation of restorable materials

A stochastic model for the circulation of restorable materials

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Article ID: iaor1989839
Country: Germany
Volume: 12
Start Page Number: 35
End Page Number: 41
Publication Date: Jan 1990
Journal: OR Spektrum
Authors:
Abstract:

A stochastic model for the circulation of restorable materials is presented. A fixed portion of the material which is distributed as the n-th time instant is assumed to be returned at the end of the n-th period and can thereafter be redistributed. Let Xn be the quantity needed at time n. If the Xn are i.i.d. random variables, the accumulated amount Yn of returned material forms a Markov chain which is analyzed in detail. For uniform and exponential Xn the asymptotic distribution of Yn is found explicitly. In the exponential case also closed formulas for the distribution function of Yn are given.

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