NONBLOCKING BROADCAST SWITCHING-NETWORKS

In a broadcast connection through a multistage network, an input port can be connected to more than one output port, with the restriction that at no time can an output port be connected to more than one input port. There are broad ranges of applications for multistage networks which can realize broadcast connection requests in a nonblocking manner in the sense that a request from an idle input port to be connected to some set of idle output ports can always be satisfied without any disturbance (that is, rearrangement) of other broadcast connections already existing in the network. We present results that lead to the currently best known explicit constructions of nonblocking broadcast switching networks with limited numbers of stages relative to both crosspoint and control algorithm complexity. In three-stage versions of our designs denoted as u(m,n,r) networks, wherein there are r switch modules in each of the first and third stages, n input ports on each switch module in the first stage, and n output ports on each switch module in the third stage, we prove that if the number of switch modules in the middle stage, m, satisfies m > min(n - 1) (x + r1/x), where 1 less-than-or-equal-to x less-than-or-equal-to min {n - 1, r}, the resulting network is nonblocking for broadcast assignments. This condition on the minimum number of switch modules in the middle stage represents an improvement from O(nr) to O(n log r/log r) relative to previously known results. We also present a linear algorithm for satisfying new broadcast connection requests in the network. Finally, we compare our nonblocking broadcast networks to other nonblocking and rearrangeable broadcast networks that have been presented in the literature.