A matrix continued fraction algorithm for the multiserver repeated order queue

This paper describes a multiserver repeated order queue with an unlimited number of sources, for which the underlying queueing process can be represented as a level-dependent quasi-birth-and-death process. For calculating its steady-state probabilities, a recursive method is proposed, which generalizes the notion of a continued fraction to sequences of matrices. In addition, rigorous proofs of the ergodicity and transience condition are given.