Brief tutorial on matrix analytic methods

In this section, we provide a brief tutorial on the quasi-birth-and-death (QBD) process and matrix analytic methods for analyzing QBD processes. We will also provide an overview of the Markovian arrival process (MAP), first introduced by M. F. Neuts [135,137]. The MAP is a generalization of the PH distribution, and it represents a correlated sequence of PH distributions. In particular, we will discuss how a MAP/PH/1 queue is modeled as a QBD process.