Part I is organized into two chapters (see Figure 1.5). In
Chapter 2,
we address the first fundamental problem
in an analysis of multiserver systems, namely
``How can we map a general distribution into a combination
of exponential distributions?''
Specifically, we develop *moment matching
algorithms*, which allow us to map a general probability distribution
into a combination of exponential distributions.
Chapter 3 is the heart of this thesis, and here
we address the second fundamental problem in an analysis of
multiserver systems, namely ``How can we analyze Markov chains on
multidimensionally infinite state spaces?''
Specifically, we introduce *dimensionality
reduction* (DR), which allows us to analyze a class of
multidimensional Markov chains that
can model many multiserver systems
with resource sharing or job prioritization.
The moment matching algorithm is also used in a key step of DR.

Takayuki Osogami 2005-07-19