Adaptive wormhole routing in tori with faults: A mathematical approach

Fault-tolerance in a communication network is defined as the ability of the network to effectively utilize its redundancy in the presence of faulty components (i.e., nodes or links). New technologies of integration now enable the design of computing systems with hundreds and even thousands of independent processing elements which can cooperate on the solution of the same problem for a corresponding improvement in the execution time. However, as the number of processing units increases, concerns for reliability and continued operation of the system in the presence of failures must be addressed. Adaptive routing algorithms have been frequently suggested as a means of improving communication performance in large-scale massively parallel computers, Multiprocessors System-on-Chip (MP-SoCs), and peer-to-peer communication networks. Before such schemes can be successfully incorporated in networks, it is necessary to have a clear understanding of the factors which affect their performance potential. This paper proposes a novel analytical model to investigate the performance of five prominent adaptive routings in wormhole-switched 2-D tori fortified with an effective scheme suggested by Chalasani and Boppana [S. Chalasani, R.V. Boppana, Adaptive wormhole routing in tori with faults, IEE Proc. Comput. Digit. Tech. 42(6) (1995) 386–394], as an instance of a fault-tolerant method widely used in the literature to achieve high adaptivity and support inter-processor communications in parallel computers. Analytical approximations of the model are confirmed by comparing them with those obtained through simulation experiments.