BMAP/G/1-Queues: Properties of the Fundamental-Period-Matrix G

One of the core problems in analyzing queues with batch Markovian arrival pro-cesses is the efficient computation of the fundamental-period-matrix G. In order to provide additio-nal insights into the relationsships between the various determinative matrices of those systems, we show that certain commutativity properties lead to an elegant proof of the exponential form of the matrix G, and that consequent exploitation of convolution properties allow a much more useful representation of the component matrices of G, thereby providing another and more efficient me-thod for its computation for a subclass of BMAP/G/1 queues.