Markov chain analysis of packet-switched banyans with arbitrary switch sizes, queue sizes, link multiplicities and speedups

Approximate Markov chains for the performance of banyan networks built with basic switches of arbitrary size containing input queues, output queues or a combination of input buffers and output queues are presented. These chains are also extended to model banyans where each link is replaced by a number of parallel links. Comparison with simulations indicates that the chains are reasonably accurate for practical network loads. It is shown that banyans built with switches containing a combination of single input buffers and output queues outperforms banyans built with switches containing only input queues or only output queues. Banyans built with larger nodes are shown to outperform banyans built with smaller nodes. It is shown that banyan-based networks with multiple links can be designed to have extremely low blocking probabilities