Design and analysis of even-sized binary shuffle-exchange networks for multiprocessors

The architecture and performance of binary shuffle-exchange networks of any size are investigated. It is established that a network with a shuffle-exchange stages whose number equals the least integer ⩾log₂N or a single recirculating stage can provide the connectivity between N inputs and N outputs using a distributed tag-based control algorithm. Control tags depend on both source and destination when N is not a power of two and can be computed in a simple manner. Several structural and dynamic properties of the network are established, contrasting the behavior of the power-of-two and composite sized systems. The performance of the network in a stochastic environment is investigated analytically. It is shown that the shuffle-exchange networks behave in much the same way with respect to traffic and buffer capacity regardless of whether the system size is a power of two or not