  The routing algorithms for parallel computers, on-chip networks, multi-core
processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router
failures must be able to handle interconnect router failures that render a
symmetrical mesh non-symmetrically. When developing a routing methodology, the
time complexity of calculation should be minimal, and thus complicated routing
strategies to introduce profitable paths may not be appropriate. Several
reports have been released in the literature on using the concept of fault
rings to provide detour paths to messages blocked by faults and to route
messages around the fault regions. In order to analyze the performance of such
algorithms, it is required to investigate the characteristics of fault rings.
In this paper, we introduce a novel performance index of network reliability
presenting the probability of message facing fault rings, and evaluating the
performance-related reliability of adaptive routing schemes in n-D mesh-based
interconnection networks with a variety of common cause fault patterns.
Sufficient simulation results of Monte-Carlo method are conducted to
demonstrate the correctness of the proposed analytical model.
