Failure dependent bandwidth in shuffle-exchange networks

A failure-dependent bandwidth model for shuffle-exchange (S/E) and augmented shuffle-exchange (S/E+) interconnection networks is presented. The models are based on probabilities of either data or address model failures for the individual binary switches that comprise the network and give the expected bandwidth as a function of the probability of failures in these switches. A model consistent with those previously published for a zero probability of failure is first developed for the S/E network. It is extended to the S/E+ network by developing a special model for the input stage of the S/E+ network and then proving that, to within a close approximation, the conditions necessary for the S/E model hold at the outputs of first stage of the S/E+. The primary uses of the bandwidth models presented are as a network design parameter and as a measure to evaluate the cost effectiveness of proposed, switch-level, reliability enhancement