Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering |
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| Institution: | 1. Department of Industrial and Business Management, Chang Gung University, Taoyuan, Taiwan;2. Systems Engineering and Operations Research Department, George Mason University, Fairfax, VA, United States of America;3. Machine Learning Lab of Alibaba, Hangzhou, China;4. School of ME, Shanghai Jiao Tong University, Shanghai, China;1. Economics and Management School, Wuhan University, Wuhan, China;2. School of Management, Huazhong University of Science and Technology, Wuhan, China;3. School of Business, Macau University of Science and Technology, Taipa, Macau |
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| Abstract: | This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the first numerical results with the type of algorithm discussed. The given two-level algorithm uses aggregation and stochastic comparison with the strong stochastic (st) order. In order to improve accuracy, it employs reordering of states and a better componentwise probability bounding algorithm given st upper- and lower-bounding probability vectors. Results in sparse storage show that there are cases in which the given algorithm proves to be useful. |
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