A simple eigenvalue method for low-order D-BMAP/G/1 queues

This paper is aimed at those engineers and practitioners who need a simple and understandable non-matrix-analytic procedure to compute the performance measures of the discrete-time BMAP/G/1 queueing system when the order of parameter matrices is very low. We develop a set of system equations and derive the vector generating function of the queue length. Starting from the generating function, we propose a eigenvalue approach that can be implemented by those who have basic knowledge on M/G/1 queues and eigenvalue algebra.