Storage Processes with Markov Additive Input and Output

We consider a storage process to which both input and output are Markov additive processes defined on the same driving Markov process X. We study the process (X, W) where W is the content of the system.

This paper has two main parts. The first uses excursion theory of Markov processes to study ladder processes of Markov additive processes (not necessarily arising from storage processes). This analysis enables us to find conditions for the existence of a limiting distribution for the Markov process (X, W). The second part uses a representation of the invariant measure for (X, W) to study the problem of level crossings of the content process W.