PhD ThesisThis thesis is concerned with the analytical modelling of computing and other discrete
event systems, for steady state performance and dependability. That is carried
out using a novel solution technique, known as the spectral expansion method. The
type of problems considered, and the systems analysed, are represented by certain
two-dimensional Markov-processes on finite or semi-infinite lattice strips. A sub set
of these Markov processes are the Quasi-Birth-and-Death processes.
These models are important because they have wide ranging applications in
the design and analysis of modern communications, advanced computing systems,
flexible manufacturing systems and in dependability modelling. Though the matrixgeometric
method is the presently most popular method, in this area, it suffers from
certain drawbacks, as illustrated in one of the chapters. Spectral expansion clearly
rises above those limitations. This also, is shown with the aid of examples.
The contributions of this thesis can be divided into two categories. They are,
• The theoretical foundation of the spectral expansion method is laid. Stability
analysis of these Markov processes is carried out. Efficient numerical solution
algorithms are developed. A comparative study is performed to show that the
spectral expansion algorithm has an edge over the matrix-geometric method,
in computational efficiency, accuracy and ease of use.
• The method is applied to several non-trivial and complicated modelling problems, occuring in computer and communication systems. Performance measures
are evaluated and optimisation issues are addressed