Performance and reliability modelling of computing systems using spectral expansion
This 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.