Investigation of Numerical Performance of Partitioning and Parallel Processing of Markov Chain (PPMC) for Complex Design Problems

Divide-and-conquer strategies have been utilized to perform evaluation calculations of complex network systems, such as reliability analysis of a Markov chain. This paper focuses on partitioning of Markov chain for a multi-modular redundant system and the fast calculation using parallel processing. The complexity of Markov chain is first reduced by eliminating the connections with low transition probabilities associated with a threshold parameter. The transition probability matrix is then reordered and partitioned such that a worse-case reliability is evaluated through the calculations in only the diagonal sub-matrices of the transition probability matrix. Since the calculations of the sub-matrices are independent to each other, the numerical efficiency can be greatly improved using parallel computing. The numerical results showed the selection of threshold parameter is a key factor to numerical efficiency. In this paper, the sensitivity of the numerical performance of Partitioning and Parallel-processing of Markov Chain (PPMC) to the threshold parameter has been investigated and discussed.