A Limit of Crosspoint Number

This paper describes a theoretical limitation on the number of crosspoints in large scale switching networks. The conclusion is as follows: given any blocking rate({\neq}0, 1), and any\epsilon > 0, we can construct a network with less crosspoints thanX_{A} (1 +{\epsilon}), whereX_{A} = 10.90 A \log_{e}A, and cannot with less crosspoints thanX_A, when the size of the network, as well as the total trafficA, becomes sufficiently large.