Lower bound on number of planes for vertically stacked optical banyan networks with link failures

Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the good properties of banyan network structures (such as the small depth and self-routing capability). Crosstalk between optical signals passing through the same DC is an intrinsic drawback in DC-based optical networks. Vertical stacking of multiple copies (planes) of an optical banyan network, namely vertically stacked optical banyan (VSOB) network, can remove the crosstalk problem in switch network, and can also make the network nonblocking. This paper deals with the blocking behavior of VSOB networks when some links are broken or failed. We found the approximate value for lower bound on number of planes required to make a VSOB networks nonblocking allowing link-failures. We have an interesting finding that the blocking probability of the VSOB networks does not always increase with the increase of link-failures; blocking probability decreases for certain range of link-failures, and then increases again. As far as we know that for switching networks, such fluctuating variation of blocking probability with the increase of link failures rate deserves special attention in switch design.