Testing the dynamic full access property of a class of multistage interconnection networks

The banyan network, and networks topologically equivalent to it, have recently been adopted as interconnection networks in multiprocessor systems. Often, a multiprocessor system is reconfigured when the banyan network becomes faulty. It is possible to avoid a complicated reconfiguration process as long as the faulty banyan network still possesses the dynamic full access (DFA) property. In this paper, we determine a necessary and sufficient condition for a faulty banyan network to possess the DFA property and design a test procedure based on the condition. The test procedure can be used to decompose a faulty banyan network into subsystems possessing the DFA property. We also evaluate the probability that a banyan network loses the DFA property, given the number of faulty switching elements. It is found that as long as faults do not occur in switching elements located in the first and last stages, this probability is very small, even when there are quite a few faulty switching elements