The rest of this chapter is organized as follows.
Section 3.2 provides a brief tutorial on the QBD
process and matrix analytic methods for analyzing the QBD process.
For the purpose of understanding the rest of the chapter, one only
needs to understand the definitions of the QBD process. In
Section 3.3, we review the state of the art in the
analysis of multidimensional Markov chains. In
Section 3.4, we define the FB, RFB, and GFB processes
and provide many examples of multiserver systems that can be modeled
as these processes. In Section 3.5, we analyze the FB, RFB,
and GFB processes via DR. In Section 3.6, we
introduce approximations in DR which reduce the computational
complexity.
In Sections 3.5-3.6, we analyze the *stationary probabilities* is the FB, RFB, and GFB processes.
Some technical details in DR are postponed to Section 3.7.
In Section 3.8, we discuss how the stationary probabilities
in the FB, RFB, and GFB processes can be translated into performance measures
such as the mean and variance of response time and queue length.
In Section 3.9, we evaluate the
accuracy and running time of DR and its approximations.