On the Communication Throughput of Buuered Multistage Interconnection Networks

Multistage networks (MIN) are used as interconnection structure in a large number of applications. Their performance is mainly determined by their communication throughput which, in most cases, has to be investigated by time-consuming simulations or approximated by simple models. In this paper, we investigate the steady state through-put of single buuered multistage interconnection networks using the so called relaxed blocking model, where a message is deleted, if the receiving buuer is occupied. We derive upper and lower bounds on the throughput of MINs of arbitrary height and show that the throughput of single-buuered networks is an order of magnitude higher than the throughput of non-buuered MINs. In detail we show, that the throughput is (n= p log n) if n is the size of the network. Because the time-dynamic of nite buuered MINs deees each marcov-or semi-marcov approach, we analyze the the equilibrium-situation of the network and give tight upper and lower bounds on the steady state distribution of I/O-sequences.