Research on Fault-tolerant Routing with High Success Probability in Mesh Interconnection Networks and Image

Mesh networks have been applied to build large scale multicomputer systems and Network-on-Chips (NoCs) extensively. Mesh networks perform poorly in tolerating faults in the view of worst-case analysis, so it is practically important for multicomputer systems and NoCs manufactures to determine that how much success probability to construct a fault-free path between two non-faulty nodes for the mesh network when the node failure probability and the network size are given. In this paper, we mainly focus on faulttolerant routing algorithm on mesh networks from probabilistic view, and provide a probabilistic method for studying routing algorithm. We propose two simple and novel routing algorithms based on the concept of k-submesh. We apply probabilistic analysis on the fault tolerance of our routing algorithms. Suppose that each node fails independently with given probability, we can derive the probability that our routing algorithms successfully return a fault-free routing path. For example, we formally prove that our routing algorithms succeed in finding a fault-free routing path with success probability at least 99% for a mesh network of up to twenty-thousand nodes as long as the node failure probability is bounded by 1.87%. Our routing algorithms run in liner time. Simulation results show that the length of the routing paths constructed by our algorithms is very close to the optimal length. On the other hand, the results also show that the multicomputer systems and NoCs based on mesh networks are quite reliable and trustable in theory and practice.