On the Probability of Facing Fault Patterns: A Performance and Comparison Measure of Network Fault-Tolerance

An important issue in the design and deployment of interconnection networks is the issue of network fault-tolerance for various types of failures. In designing parallel processing using torus as the underlying interconnection topology as well as in designing real applications on such processors, the estimates of the network reliability and fault-tolerance are important in choosing the routing algorithms and predicting their performance in the presence of faulty nodes. Under node-failure model, the faulty nodes may coalesce into fault patterns, which classified into two major categories, i.e., convex (|-shaped, $\Box$-shaped) and concave (L-shaped, T-shaped, +-shaped, H-shaped, U-shaped) regions. In this correspondence, we propose the first solution for computing the probability of message facing the fault patterns in tori both for convex and concave regions that is verified using simulation experiments. Our approach works for any number of faults as long as the network remains connected. We use these models to measure the network faulttolerance that can be achieved by adaptive routings, and to assess the impact of various fault patterns on the performance of such networks.