A spectral approach to compute the mean performance measures of the queue with low-order BMAP input

This paper targets engineers and practitioners who want a simple procedure to compute the mean performance measures of the Batch Markovian Arrival process (BMAP/G/1) queueing system when the parameter matrices order 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 spectral approach that can be understandable to those who have basic knowledge of M/G/1 queues and eigenvalue algebra.