On Number of Planes of Rearrangeably Nonblocking Optical Banyan Networks with Link Failures

Abstract

Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the desirable properties (such as the small depth and self-routing capability) of banyan network structures. Although banyan-type networks result in severe blocking and crosstalk, both these problems can be minimized by using sufficient number of banyan planes in the VSOB network structure. The number of banyan planes is minimum for rearrangeably nonblocking and maximum for strictly nonblocking structure. Both results are available for VSOB networks when there exist no internal link-failures. Since the issue of link-failure is unavoidable, we intend to find the minimum number of planes required to make a VSOB network nonblocking when some links are broken or failed in the structure. This paper presents the approximate number of planes required to make a VSOB networks rearrangeably nonblocking allowing link-failures. We also show an interesting behavior of the blocking probability of a faulty VSOB networks that the blocking probability may not always increase monotonously with the increase of link-failures; blocking probability decreases for certain range of link-failures, and then increases again. We believe that such fluctuating behavior of blocking probability with the increase of link failure probability deserves special attention in switch design.  Keywords: Banyan networks; Blocking probability; Switching networks; Vertical stacking; Link-failures. © 2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1070