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Organization of this chapter

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.


next up previous contents
Next: Brief tutorial on matrix Up: Overview Previous: RFB and GFB processes   Contents
Takayuki Osogami 2005-07-19