A new performance measure for characterizing fault rings in interconnection networks

One of the fundamental issues in parallel computers is how to efficiently perform routing in a faulty network where each component fails with some probability. Adaptive fault-tolerant routing algorithms in such systems have been frequently suggested as a means of providing continuous operations in the presence of one or more failures by allowing the graceful system degradation. Many algorithms involve adding buffer space and complex control logic to the routing nodes. However, the addition of extra logic circuits and buffer space makes nodes more liable to failure and less reliable. Further, if the shape of fault pattern is confined, then many non-faulty nodes will be sacrificed and hence their resources are wasted. This is clearly an undesirable solution and motivates solutions that provoke efficient use of non-faulty nodes. One such approach to reducing the number of functional nodes that must be marked as faulty is based on the concept of fault rings to support more flexible routing around rectangular fault regions. Before such schemes can be successfully incorporated in networks, it is necessary to have a clear understanding of the factors that affect their performance potential. In this paper, we propose the first general solution for computing the probability of message facing the fault rings with and without overlapping in the well-known torus networks. We also conduct extensive simulation experiments using various fault patterns, the results of which are used to confirm the good accuracy of the proposed analytical models.