Characterization of spatial fault patterns in interconnection networks

Parallel computers, such as multiprocessors system-on-chip (Mp-SoCs), multicomputers and cluster computers, are consisting of hundreds or thousands multiple processing units and components (such as routers, channels and connectors) connected via some interconnection network that collectively may undergo high failure rates. Therefore, these systems are required to be equipped with fault-tolerant mechanisms to ensure that the system will keep running in a degraded mode. Normally, the faulty components are coalesced into fault regions, which are classified into two major categories: convex and concave regions. In this paper, we propose the first solution to calculate the probability of occurrences of common fault patterns in torus and mesh interconnection networks which includes both convex (-shaped, □-shaped) and concave (L-shaped, T-shaped, +-shaped, H-shaped) regions. These results play a key role when studying, particularly, the performance analysis of routing algorithms proposed for interconnection networks under faulty conditions.