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The Renewal Equation for Markov Renewal Processes with Applications to Storage Models.

Eric S. Tollar

Abstract

For Markov renewal process in which the sojourn times are controlled by an imbedded, denumerable state Markov chain, it is shown that there exist a random time at which the Markov renewal process regenerates. The basic renewal theorem is applied to determine the limiting behavior of the Markov renewal process. These results are then applied to a particular two compartment storage model to determine the limiting behavior of the amounts in storage. Keywords: Markov Renewal Process; Semi-Markov Process; Renewal Equation; Coupling; Storage Model.

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Key concepts: Markov chain, Markov renewal process, Renewal theory, Computer science, Markov model, Markov process, Mathematics, Variable-order Markov model