Probabilistic Reliability via Subsystem Structures of Arrangement Graph Networks

作     者：Huang, Yanze Lin, Limei Xu, Li Hsieh, Sun-Yuan 

作者机构：Fujian University of Technology Fujian Provincial Key Laboratory of Big Data Mining and Applications School of Computer Science and Mathematics Fuzhou350118 China Fujian Normal University College of Computer and Cyber Security Key Laboratory of Network Security and Cryptology Fuzhou350117 China National Cheng Kung University Department of Computer Science and Information Engineering Tainan701 Taiwan 

出 版 物：《IEEE Transactions on Reliability》 (IEEE Trans Reliab)

年 卷 期：2024年第73卷第1期

页      面：279-289页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0835[工学-软件工程] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 081202[工学-计算机软件与理论] 

基　　金：This work was supported in part by the National Natural Science Foundation of China under Grant 62102088  Grant 62171132  Grant U1905211  Grant 61771140  and Grant 61773415  in part by the Fok Ying Tung Education Foundation under Grant 171061  and in part by the Natural Science Foundation of Fujian Province under Grant 2021J05228 

主　　题：Fault tolerance 

摘      要：With the rapid growth of the number of processors in a multiprocessor system, faulty processors occur in it with a probability that rises quickly. The probability of a subsystem with an appropriate size being fault-free in a definite time interval is a significant and practical measure of the reliability for a multiprocessor system, which characterizes the functionality of a multiprocessor system well. Motivated by the study of subgraph reliability, as well as the attractive structure and fault tolerance properties of (n, k)-arrangement graph A n, k, we focus on the subgraph reliability for A n, k under the probabilistic fault model in this article. First, we investigate intersections of no more than four subgraphs in A n, k, and classify all the intersecting modes. Second, we focus on the probability P(q, A n, k n-1, k-1) with which at least one (n-1, k-1)-subarrangement graph is fault-free in A n, k, when given a uniform probability q with which a single vertex is fault-free, and we establish the P(q, A n, kn-1, k-1) by adopting the principle of inclusion-exclusion under the probabilistic fault model. Finally, we study the probabilistic fault model involving a nonuniform probability with which a single vertex is fault-free, and we prove that the P(q, A n, kn-1, k-1) under both models is very close to the asymptotic value by both theoretical arguments and experimental results. © 1963-2012 IEEE.