Dynamic routing in grid-connected networks

This dissertation describes the effect of collection and distribution of fault information on routing capacity in grid-connected networks with faults occurring during the routing process. The grid-connected network, such as hypercubes, 2-D meshes, and 3-D meshes, is one of the simplest and least expensive structures to build a system using hundreds and even thousands of processors. In such a system, efficient communication among the processors is critical to performance. Hence, the routing of messages is an important issue that needs to be addressed. As the number of nodes in the networks increases, the chance of failure also increases. The complex nature of networks also makes them vulnerable to disturbances. Therefore, the ability to route messages efficiently in the presence of faulty components, especially those might occur during the routing process, is becoming increasingly important. A central issue in designing a fault-tolerant routing algorithm is the way fault information is collected and used. The safety level model is a special coded fault information model in hypercubes which is more cost effective and more efficient than other information models. In this model, each node is associated with an integer, called safety level, which is an approximated measure of the number and distribution of faulty nodes in the neighborhood. The safety level of each node in an n-dimensional hypercube can be easily calculated through (n - 1)-rounds information exchanges among neighboring nodes. A k-safe node indicates the existence of at least one Hamming distance path (also called optimal path or minimal path) from this node to any node with Hamming distance k. We focus on routing capacity using safety levels in a dynamic system. In this case, the update of safety levels and the routing process proceed hand-in-hand. During the converging period, the routing process may experience extra hops based on unstable (inconsistent) information. Under the assumption that the total number of faults is less than n, we provide an upper bound of extra hops and show its accuracy and effectiveness. After that, we extend the results to meshes. Our simulation results show the effectiveness of our information model and scalability of our fault-information-based routing in the grid-connected networks with dynamic faults. Because our information is easy to update and maintain and optimality is still preserved, it is more cost effective than the others.