Lower bound on blocking probability for vertically stacked optical banyan networks with given crosstalk constraint

Vertical stacking of multiple copies of an optical banyan network is a novel scheme for building nonblocking optical switching networks. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves all the properties of the banyan network, but increases the hardware cost significantly under first order crosstalk-free constraint. Therefore, blocking behavior analysis could be an effective approach to studying network performance, and finding a graceful compromise between hardware costs and blocking probability with different degree of crosstalk constraint. However, lower bound on number of planes for such networks with zero crosstalk constraint has been determined previously. In this paper, we present the simulation results for lower bound on blocking probability with given degree of crosstalk. The results show that blocking probability decreases to low value if we allow some CSEs to the network. The simulation results presented in this paper can guide network designer in finding a tradeoff among the blocking probability, and the degree of crosstalk of VSOB networks.