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 than
X_{A} (1 +{\epsilon})
, where
X_{A} = 10.90 A \log_{e}A
, and cannot with less crosspoints than
X_A
, when the size of the network, as well as the total traffic
A
, becomes sufficiently large.