Analytical models for the performance analysis of banyan networks

Banyan networks are an important class of multistage interconnection networks that have been used for connecting processors with memories in parallel machines. This dissertation presents two models that can be used for the performance evaluation of such networks. The first model uses Markov chains to approximate the flow processes in the network. We provide accurate methods for predicting the delay and throughput for packets in non-combining and combining Banyan networks with uniform traffic and non-uniform traffic, with fixed service times and varying service times, and with finite buffers and infinite buffers. Using this approximation, we also present a method based on the technique of coupling to estimate a bound on the time for a Banyan network starting empty to approach steady state. The second model approximates the flow processes with Brownian motions and yields good estimates for delay and queue lengths under heavy traffic.