Testing the Dynamic Full Access Property of a Class of Multistage Interconnection Networks

A banyan network and its topologically equivalent ones have recently been adopted as the interconnection networks in a multiprocessor system. 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 short note, we determine a necessary and sufficient condition for a faulty banyan network to possess the DFA property and design a testing procedure based on the condition. The testing 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. I t is found that as long as faults do not occur in switching elements located in the first and the last stages, this probability is very small, even when there are quite a few faulty switching elements. Zndex Terms-Multiprocessor system, multistage interconnection networks, fault tolerance, dynamic full access