An alternative approach for analyzing finite buffer queues in discrete time

In this paper, we present a novel use of matrix-analytic method (MAM) for analyzing the GI/G/1/K system. The novelty is based on an unconventional arrangement of the state space and also a Markov-based representation of the arrival and service processes with at least one of them based on the elapsed time approach. This results in a matrix-product form solution, because the resulting Markov chain is level-dependent. We therefore end up with rate matrices which are level-dependent. The resulting matrices are explicitly determined. We show that stationary distributions can be determined explicitly. An illustrative example is presented. We discuss some special cases such as GI/Geo/1/K and Geo/G/1/K and show extensions to the GIX/G/1/K and the GI/Geo/c/K systems.