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# FB, RFB, and GFB processes

In this section, we define the foreground-background (FB) process, the recursive FB (RFB) process, and the generalized FB (GFB) process, and provide examples of these processes. In the rest of this chapter, we denote a matrix by a bold face letter such as and its element by , and we use to denote a vector and to denote its -th element. Also, we use matrix to denote the generator matrix of a QBD process characterized by parameter .'' Here, may be a single letter or number, denoting process or the -th QBD process, or may be a pair of numbers , denoting the -th QBD process of type . Unless otherwise stated, we express using submatrices, , , and , such that

where encodes (local) transitions within level , encodes (forward) transitions from level to level , and encodes (backward) transitions from level to level , for each (see Section 3.2).

Subsections

Next: Definition of FB process Up: Dimensionality reduction of Markov Previous: Other approaches   Contents
Takayuki Osogami 2005-07-19