Coarse-Grained Parallel Uniformization for Continuous-Time Markov Chains

Abstract

This paper discusses parallel algorithms for transient analysis of continuous-time Markov chains (CTMCs). In dependable computing, it is used for evaluating the rare events such as failure based on CTMC models. The uniformizaton is a well-known algorithm for obtaining the transient solution of CTMC. However, the computation cost of uniformization is not low in the case of large-sized and stiff CTMCs. This paper considers parallelization of the uniformization algorithm. Particularly, we propose a coarse-grained parallel uniformization which is appropriate for multicore processors. This method enables us to analyze the large-sized and stiff CTMCs efficiently. In numerical examples, we examine the effectiveness of the proposed parallel algorithms with multicore processors.