On a duality between a non-Markovian storage/production process and a Markovian dam process with state-dependent input and output

On a duality between a non-Markovian storage/production process and a Markovian dam process with state-dependent input and output

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Article ID: iaor1990523
Country: Israel
Volume: 26
Issue: 4
Start Page Number: 1
End Page Number: 7
Publication Date: Dec 1989
Journal: Journal of Applied Probability
Authors: ,
Abstract:

The authors consider a storage/production process where the production rate is state dependent, the demand arrival is a renewal process, and the sizes of the demands are i.i.d exponentially distributed random variables. The resulting content process is non-Markovian but regenerative. We construct a dual Markovian dam process with drift, jump rate and jump sizes that are state dependent and use it to compute the limiting one-dimensional distribution of the content process.

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