A Thory of Fault-Tolerant routing in Wormhole Networks

Fault-tolerant systems aim at providing continuous operation in the presence of faults. Multicomputers rely on an interconnection network between processors to support the message-passing mechanism. Therefore, the reliability of the interconnection network is very important for the reliability of the whole system. This paper analyzes the effective redundancy available in a wormhole network by combining connectivity and deadlock freedom. Redundancy is defined at the channel level. We propose a sufficient condition for channel redundancy, also computing the set of redundant channels. The redundancy level of the network is also defined, proposing a theorem that supplies its value. This theory is developed on top of our necessary and sufficient condition for deadlock-free adaptive routing. The new theory also considers the failure of physical channels when virtual channels are used. Finally, we propose a methodology for the design of fault-tolerant routing algorithms, showing its application to n-dimensional meshes.