On the limit behavior of a multicompartment storage model with an underlying Markov chain

Abstract

The present paper considers a multicompartment storage model with one-way flow. The inputs and outputs for each compartment are controlled by a denumerable-state Markov chain. Assuming finite first and second moments, it is shown that the amounts of material in certain compartments converge in distribution while for others they diverge, based on appropriate first-moment conditions on the inputs and outputs. It is also shown that the diverging compartments under suitable normalization converge to functionals of Brownian motion, independent of those compartments which converge without normalization.