Optimum multidimensional tori based on low-port routers and hubs

A method for constructing optimal system networks with the topology of multidimensional tori is considered. The optimization was performed according to such important functional characteristics of the network as the number of its subscribers (processors) and transmission delays between them, set by the network diameter. Optimization was carried out in the element base of low-port routers and splitters of duplex channels (hubs) by using networks with the topology of quasi-complete graphs. Optimization is realized due to the invariant expansion of the multidimensional torus and the duplex channel with preservation of their route properties such as the routing method and maximum transmission delays (network diameter). It is shown that optimization leads to an increase in the number of subscribers with constant delays and to a reduction in delays with a constant number of subscribers. Optimization is accompanied by some complication of the network in terms of circuit and cable costs. In this case, the measure of complication (expressed in the number of times) is less than the measure of joint improvement of both characteristics. The comparative characteristics of the optimal tori and tori of the Angara domestic system network are given. A substantial increase in the number of subscribers and a decrease in the diameters of optimal tori in comparison with the Angara network have been proven.