الملخص الإنجليزي
The use of large scale Markov chains participate extensively in many different disciplines, such as biological, chemical, physical and social science as well as in business and engineering. In many cases, generated models are complex and very large which, in turn, poses a number of challenges in terms of memory requirements and computation time. Parallel computing techniques provide a good alternative to overcome such constraints. However, to take the advantage of Parallel computation we required to ensure the communication between the processors is reduced as minimum as possible. In this report, the concern of the memory requirement is addressed by using a distributed memory machine and sparse representation. A new Aggregation Isolation algorithm (AI) has been studied and a sparse sequential version has been implemented to solve the both computation as well as memory storage requirements. In this thesis, a parallel sparse version of the Al algorithm (PAI) has been proposed and developed. Our experimental study shows that for the tested model the convergence rate of PAI is slower than: Al. This can be explained by the presence of a very strong Gauss-Seidel effect in AI algorithm which is lost in the parallel version PAI which has been implemented on the Sultan Qaboos University High Performance Computer (HPC) system
