Analysis of banyan networks offered traffic with geometrically distributed message lengths

An analysis of finite-input-buffered banyan networks offered traffic having geometrically distributed message lengths is presented. This is one of the few multistage-network analyses for networks offered non-unit-length messages and is the only one that the authors are aware of for finite-input-buffered banyan networks. In the analysis, network switching elements are modelled using two state machines, one for queue heads, the other for entire queues. A network is modelled using one switching-element model to represent each stage. Together these model the effect that non-unit-length messages have on banyans. Solutions are obtained iteratively. Network performance figures were obtained with this analysis and compared to simulation results. The figures show that the analysis can predict the effect of message length on throughput and delay, including the performance degradation caused by longer messages